[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=12\\ h=45 \end{cases}\implies V=\cfrac{\pi (12)^2(45)}{3}\implies V=2160\pi[/tex]
Find the x- and y-intercept of the line. x + 4y = 36 x-intercept is 36; y-intercept is 9. x-intercept is 1; y-intercept is 4. x-intercept is 9; y-intercept is 36. x-intercept is 4; y-intercept is 1.
Answer:
see explanation
Step-by-step explanation:
Given
x + 4y = 36
To find the x- intercept, let y = 0 in the equation and solve for x
x + 0 = 36 ⇒ x = 36 ← x- intercept
To find the y- intercept let x = 0 in the equation and solve for y
0 + 4y = 36 ⇒ y = 9 ← y- intercept
Answer:
x-intercept is 36; y-intercept is 9.
Step-by-step explanation:
Given equation of the line,
[tex]x+4y=36[/tex]
For x-intercept ( the point at which the line intersects the x-axis ),
y = 0,
[tex]\implies x+4(0) = 36[/tex]
[tex]x=36[/tex]
⇒ The value of x-intercept is 36,
Now, for y-intercept( the point at which the line interests the y-axis )
x = 0,
0 + 4y = 36
⇒ y = 9
⇒ The value of y-intercept is 9.
Hence, first option is correct.
Find the volume of the pyramid below.
O A. 960 units
O B. 384 units3
O C. 480 units 3
O
D. 1152 units3
Answer:
B
Step-by-step explanation:
The volume (V) of a pyramid is calculated as
V = [tex]\frac{1}{3}[/tex] area of base × perpendicular height (h)
area of square base = 12 × 12 = 144 units² and h = 8, hence
V = [tex]\frac{1}{3}[/tex] × 144 × 8 = [tex]\frac{1152}{3}[/tex] = 384 units³ → B
Volume of the pyramid is equal to [tex]384 \ unit^{3}[/tex].
What is a volume?" Volume is defined as the total space occupied by any three- dimensional object enclosed in it."
Formula used
Volume of a pyramid [tex]= \frac{1}{3} \times Area \ of \ the \ base \times height[/tex]
Area of a square [tex]= s^{2}[/tex]
[tex]s=[/tex] Side length
According to the question,
Given dimensions of pyramid,
Height of the pyramid [tex]= 8 \ units[/tex]
Base of the pyramid is square in shape
Side length of a square [tex]= 12 \ units[/tex]
Substitute the value in the formula to get the area of the base,
Area of the base [tex]= 12 \times 12[/tex]
[tex]= 144 \ units^{2}[/tex]
Substitute the value to get the volume of the pyramid,
Volume of the pyramid [tex]= \frac{1}{3} \times 144 \times 8[/tex]
[tex]= 48 \times 8\\\\= 384 \ units^{3}[/tex]
Hence, Option(B) is the correct answer.
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Vertical? Supplementary? Right? Complementary?
Answer:
D
Step-by-step explanation:
because we know that angle EOD is less the 90 so that means that it is complementary. For AOB it is the same but we can check by adding 35 plus x plus 90 =180 degrees so 35+90=125 x=180-125=55 so x=55 and 55 is less then 90 so it is a complementary angle.
Please help.
m.XYZ =
radians. Covert this radian measure to its equivalent measure in degrees.
Answer:
Multiply 5π/6 by 180/π, you will get answer 150°.
Answer: [tex]150^{\circ}[/tex]
Step-by-step explanation:
To convert a radian measure to degrees , we generally multiply it by 180° and divide it by [tex]\pi[/tex].
Given : [tex]m. \overarc{XYZ}=\dfrac{5\pi}{6}\text{radian}[/tex]
Then, In degrees it should be
[tex]m. \overarc{XYZ}=\dfrac{5\pi}{6}\times\dfrac{180^{\circ}}{\pi}\\\\\Rightarrow m.\overarc{XYZ}=150^{\circ}[/tex]
Hence, the correct answer is [tex]150^{\circ}[/tex].
What is the diameter of the circle?
[1] units
ANSWER
The diameter is 8 units.
EXPLANATION
A portion of the y-axis is serving as the diameter of the circle.
The portion of the y-axis that intersects the circle at two points.
We can use these intercepts to find the diameter.
There is a y-intercept at y=2 and y=-6.
The distance between the two intercepts is the diameter of the circle.
[tex] |2 - - 6| = |2 + 6| = 8[/tex]
Therefore the radius is 8 units.
Answer: [tex]diameter=8\ units[/tex]
Step-by-step explanation:
By definition, the radius of a circle is the distance from its center to its edge.
We need to remember that diameter of a circle is twice the radius:
[tex]diameter=2(radius)[/tex]
Then, you can observe in the figure that there are 4 units between the center of this circle and its edge, therefore the radius is:
[tex]radius=4\ units[/tex]
Finally, you need to substitute the radius calculated into the formula [tex]diameter=2*radius[/tex] to find the value of the diameter of this circle. Then, this is:
[tex]diameter=2(4\ units)[/tex]
[tex]diameter=8\ units[/tex]
Which is not an equation of the line that passes through the points (1, 1) and (5, 5)?
The correct answer is option d) ( y = -x + 2 ).
Let's analyze each option to determine which equation does not represent the line passing through the points (1, 1) and (5, 5).
a) ( y = x ): This equation represents a line with a slope of 1 and passes through the origin. To check if it passes through (1, 1) and (5, 5), we substitute the coordinates into the equation:
- For (1, 1): ( 1 = 1 ) (True)
- For (5, 5): ( 5 = 5 ) (True)
The equation ( y = x ) is consistent with the given points.
b) ( y = 2x - 1 ): This equation represents a line with a slope of 2 and a y-intercept of -1. Checking with the given points:
- For (1, 1): ( 1 = 2(1) - 1 ) (True)
- For (5, 5): ( 5 = 2(5) - 1 ) (True)
The equation ( y = 2x - 1 ) is consistent with the given points.
c) ( 2y = 2x ): This equation can be simplified to ( y = x ), which we have already determined is consistent with the points.
d) ( y = -x + 2 ): Checking with the given points:
- For (1, 1): ( 1 = -1 + 2 ) (True)
- For (5, 5): ( 5 = -5 + 2 ) (False)
The equation ( y = -x + 2 ) does not pass through the point (5, 5).
QUESTION
Which of the following equations does not represent the line passing through the points (1, 1) and (5, 5)?
a) ( y = x )
b) ( y = 2x - 1 )
c) ( 2y = 2x )
d) ( y = -x + 2 )
Julie is in a singing competition and needs an average score of 9.1 to make it to the next round. There are four judges. The first three judges gave scores of 8.8, 9.5, and 9.2.
What equation can you solve to determine the lowest score the fourth judge can give for Julie to move on?
Answer:
Solve the equation
[tex]\displaystyle \frac{8.8 + 9.5 + 9.2 + x}{4} \ge 9.1[/tex],
where [tex]x[/tex] is the minimum score of the fourth judge.
At least 8.9 points.
Step-by-step explanation:
Let the score of the fourth judge be [tex]x[/tex].
The average score is the sum of the four judges' score divided by the number of scores. That is:
[tex]\displaystyle \text{Average Score} = \frac{8.8 + 9.5 + 9.2 + x}{4}[/tex].
The minimum average score needs to be greater than or equal to [tex]9.1[/tex]. In other words,
[tex]\displaystyle \frac{8.8 + 9.5 + 9.2 + x}{4} \ge 9.1[/tex].
Multiply both sides of by four.
[tex]8.8 + 9.5 + 9.2 + x = 4\times 9.1[/tex].
Subtract [tex]8.8 + 9.5 + 9.2[/tex] from both sides of the equation:
[tex]x = 4\times 9.1 - (8.8 + 9.5 + 9.2) = 8.9[/tex].
In other words, the minimum score of the last judge is [tex]8.9[/tex] for Julie to move on.
The value of x is
.
Answer:
x=93
Step-by-step explanation:
The exterior angles of a triangle add to 360 degrees
133+134+x = 360
267+x =360
Subtract 267 from each side
267+x-267 = 360-267
x =93
What is the range of the discrete finite function?
Answer:
Option D
Step-by-step explanation:
The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.
In plain English, the definition means:
The range is the resulting y-values we get after substituting all the possible x-values.
How to find the range
1.The range of a function is the spread of possible y-values (minimum y-value to maximum y-value)
2. Substitute different x-values into the expression for y to see what is happening. (Ask yourself: Is y always positive? Always negative? Or maybe not equal to certain values?)
3. Make sure you look for minimum and maximum values of y.
4. Draw a sketch! In math, it's very true that a picture is worth a thousand words.
Line GH contains points (-2,6) and H (5,-3). What is the slope of GH
Answer:
-9/7
Step-by-step explanation:
To find the slope given 2 points, we use the formula
m = (y2-y1)/(x2-x1)
where (x1,y2) and (x2,y2) are the two points
m = (-3-6)/(5--2)
m = (-3-6)/(5+2)
= -9/7
Answer:
y=-1.3x+3.4
Step-by-step explanation:
What is the product of (2x - 5)(2x + 5)?
Answer:
4x2−25
Step-by-step explanation:
yes
Answer:
4x^2-25
Step-by-step explanation:
If s(x) = x - 7 and t(x) = 4x7 - X+3, which expression is equivalent to (tºs)(x)?
4(x - 72 - x - 7+3
4(x - 72 -(x-7) + 3
(4x²-x+3)-7
(4x? – x+3)(x-7)
Answer:
4(x - 7)² - (x - 7) + 3Step-by-step explanation:
[tex]s(x)=x-7,\ t(x)=4x^2-x+3\\\\(t\circ s)(x)=t\bigg(s(x)\bigg)-\text{exchange x to }\ s(x)=x-7:\\\\(t\circ s)(x)=4(x-7)^2-(x-7)+3[/tex]
Select the two values of x that are roots of this equation. (This is for apex by the way)
x^2-5x+5=0
Answer:
Step-by-step explanation:
Find the discriminant, b^2-4ac: Here a = 1, b = -5 and c = 5.
Then the discriminant is (-5)^2-4(1)(5) = 5, and so there are 2 real, different roots. The roots are:
-(-5) ±√5
x = ----------------, which correspond to answers A and C.
2(1)
The roots of the equation will be (5 - √5) / 2 and (5 + √5) / 2. Then the correct options are A and C.
What is a quadratic equation?The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2. Then we have
The quadratic equation is given below.
x² - 5x + 5 = 0
Then the root of the equation is given as
[tex]\rm x = \dfrac{ - (-5) \pm \sqrt{(-5)^2 - 4*1*5}}{2*1}\\\\x = \dfrac{5 \pm \sqrt{25-20}}{2}\\\\x = \dfrac{5 \pm \sqrt5}{2}\\\\x = \dfrac{5 - \sqrt5}{2}, \dfrac{5 + \sqrt5}{2}[/tex]
Thus, the correct options are A and C.
More about the quadratic equation link is given below.
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Find the x-intercepts of the parabola with
vertex (-3,-14) and y-intercept (0,13).
Write your answer in this form: (X1,Y1), (X2,42).
If necessary, round to the nearest hundredth.
The x-intercepts of the parabola are [tex]\(x = -3 + \sqrt{\frac{14}{3}}\) and \(x = -3 - \sqrt{\frac{14}{3}}\).[/tex]
To find the x-intercepts of the parabola, we need to set y=0 in the equation of the parabola and solve for x.
Given that the vertex of the parabola is [tex]\((-3, -14)\),[/tex] the equation of the parabola can be expressed in the form [tex]\(y = a(x - h)^2 + k\)[/tex], where [tex]\((h, k)\)[/tex]represents the vertex and a is the coefficient determining the direction and width of the parabola.
Using the vertex form, we have:
[tex]\[ y = a(x + 3)^2 - 14 \][/tex]
We know that the y-intercept is (0,13) so when x=0, y=13:
[tex]\[ 13 = a(0 + 3)^2 - 14 \]\[ 13 = a(9) - 14 \]\[ 13 = 9a - 14 \]\[ 9a = 13 + 14 \][/tex]
[tex]\[ 9a = 27 \]\[ a = \frac{27}{9} \]\[ a = 3 \][/tex]
So, the equation of the parabola is:
[tex]\[ y = 3(x + 3)^2 - 14 \][/tex]
Now, to find the x-intercepts, we set y=0:
[tex]\[ 0 = 3(x + 3)^2 - 14 \]\[ 3(x + 3)^2 = 14 \]\[ (x + 3)^2 = \frac{14}{3} \][/tex]
Now, we take the square root of both sides:
[tex]\[ x + 3 = \pm \sqrt{\frac{14}{3}} \][/tex]
Fit a quadratic function to these three points (-1, -11) (0,-3) and (3,-27)
ANSWER
[tex]y = - 4 {x}^{2} + 4x - 3[/tex]
EXPLANATION
Let the quadratic function be
[tex]y = a {x}^{2} + bx + c[/tex]
We substitute each point to find the constants, a,b, and c.
Substitute: (x=0,y=-3)
[tex] - 3 = a {(0)}^{2} + b(0) + c[/tex]
[tex] \implies \: c = - 3...(1)[/tex]
Substitute: (x=-1,y=-11) and c=-3
[tex] - 11 = a {( - 1)}^{2} + b( - 1) + - 3[/tex]
[tex] \implies \: - 11 = a - b - 3[/tex]
[tex] \implies \: a - b = - 8...(2)[/tex]
Substitute: (x=3,y=-27) and c=-3
[tex] -27= a {( 3)}^{2} + b( 3) + - 3[/tex]
[tex] \implies \: - 27 = 9a + 3b - 3[/tex]
[tex]\implies \: 3a + b = - 8...(3)[/tex]
Add equations (3) and (2)
[tex]3a + a = - 8 + - 8[/tex]
[tex]4a = - 16[/tex]
[tex]a = - 4[/tex]
Put a=-4 in equation (2)
[tex] - 4 - b = - 8[/tex]
[tex] - b = - 8 + 4 [/tex]
[tex] - b = - 4[/tex]
[tex]b = 4[/tex]
The quadratic equation is
[tex]y = - 4 {x}^{2} + 4x - 3[/tex]
Final answer:
To fit a quadratic function to the three given points, we use the general form y = ax² + bx + c and set up a system of equations. Solving the system yields the function y = -2x² + 6x - 3.
Explanation:
To fit a quadratic function to the points (-1, -11), (0, -3), and (3, -27), we need to find a function of the form y = ax² + bx + c where a, b, and c are constants. We will set up three equations based on the given points:
-11 = a(-1)² + b(-1) + c-3 = a(0)² + b(0) + c-27 = a(3)² + b(3) + cSolving these equations gives us a system:
a - b + c = -11c = -39a + 3b + c = -27From the second equation, we have c = -3. Inserting that into the first and third equations:
a - b = -89a + 3b = -24Solving this system gives us a = -2 and b = 6.
Therefore, the quadratic function fitting the points is y = -2x² + 6x - 3.
Organic apples are on special for $1.50 per pound. Does total cost vary
inversely or directly with the number of pounds purchased? Find the cost of
3.4 pounds of apples.
A. Inversely: $5.10
B. Directly; $5.10
C. Inversely: $2.27
D. Directly; $2.27
Answer:
B: Directly; $5.10
Step-by-step explanation:
1 pound of apples = $1.50
so
3.4 pounds of apples = $1.50 x 3.4
=$5.10
The soccer teams in a club league are ordering new jerseys. The cost is $18 per jersey plus $10 shipping per team.
There are 7 teams, each with an equal number of players. The total cost to order jerseys for all the teams is
$2,590. Which equation can be used to determine x, the number of players on each team?
Answer:
10*7+ 18x *7 =2590
or 70 + 18x*7 =2590
Step-by-step explanation:
10*7 to find out how much the shipping costs for the 7 teams altogether
18*x because you need to find how much the jerseys cost for all the soccer teams
then multiply it by 7 to find how many players on each team
when you solve for x you get 20
there are 20 players on each on team.
Final answer:
To determine the number of players on each soccer team, given the total jersey order cost for all teams, the equation 7(18x) + 7(10) = 2590 can be used, where x represents the number of players.
Explanation:
The question asks which equation can be used to determine x, the number of players on each team, given that the total cost to order jerseys for all the teams is $2,590, the cost per jersey is $18, and the shipping per team is $10, with 7 teams ordering. To find the equation, we first outline the total costs involved: the cost of the jerseys plus the shipping cost for all teams.
Let's denote x as the number of players on each team.
The cost for jerseys for one team would be 18x (since each jersey costs $18), and the cost to outfit all 7 teams would be 7 times that amount, plus the total shipping cost for all teams (7 teams times $10 per team).
So, the equation can be represented as:
7(18x) + 7(10) = 2590
This equation accounts for both the per-jersey cost and the fixed shipping fee for each team, totaling up to the overall cost reported.
Round 2767545 to the nearest ten
Answer:
2767550
Step-by-step explanation:
looking at the number 2767545
reading number from right to left
the most right number is 0 there that is the ones digit
next right number is 4 that is the tens digit (that is what we are rounding to. we use the one right of the ten's digit to decide to round up or not. You round up if is 5 or more. So since the ones digit is 5, that is 5 or more. so we round the 4 in the ten's to a 5 and make one's 0.
---
If someone side round to nearest hundreds: it would be 2767500 because the digit directly to the right of it was a 4
Answer:
2767550.
Step-by-step explanation:
Th ten's digit is 4 and as the units digit is 5 we round up. That gives us
2767550.
this line plot shows how many miles maya walked this week.
(please look at photo)
which shows the number of miles maya would have walked each day is she would have walked the same distance every day.
A - 9 9/14 miles
B - 9 miles
C - 8 9/14 miles
D - 8 miles
Answer:
your answer would be A -9 9/14
Probability geometry question 20 points and brainiest
Hector plans to randomly draw a card from a standard deck of cards, record the result, return the card to the deck, shuffle the deck, and randomly draw another card. So, he will draw a total of 2 cards.
What is the probability that he draws a 2, and then a 4?
Children play a form of hopscotch called Jumby. The pattern for the game is as given below.
Find the area of the pattern simplest in form.
(SHOW WORK)
Answer:
[tex]7t^2+21t[/tex]Explanation:
The pattern of the game consists on 7 congruent (necessary assumption) rectangles.
The dimensions of such congruent rectangles are given for the rectangle number 6: lenght = t + 3 (a binomial) and width = t (a monomial).
So, the area of each rectangle is found as the product of a monomial and a binomial:
[tex]t(t+3)[/tex]Apply distributive property:
[tex]t^2+3t[/tex]Since that is the area on one rectangle, you have to mulply by the number of reactangles (7):
[tex]7(t^2+3t)=7t^2+21t[/tex] ← answerAnswer:
Step-by-step explanation:
Given is a form of hopscotch called Jumby.
The pattern consists of 7 identical rectangles with length t+3 and width 5
To find area it is necessary to add the totals of all 7 rectangles
OR area = 7 * area of one rectangle
Area of one rectangle [tex]= lw \\= t(t+3)\\= t^2+3t[/tex]
Hence area of whole figure = [tex]7(t^2+3t)\\=7t^2+21t[/tex]
Giuseppi's Pizza had orders for $931.00 of pizzas. The prices were $21 for a large pizza, 514 for a medium pizza, and $7 for a small pizza. The number of large pizzas was two less than four times the number of medium pizzas. The
number of small pizzas was three more than three times the number of medium pizzas. How many of each size of pizza were ordered?
Answer:
Number of Large Pizzas: 30
Number of Medium Pizzas: 8
Number of Small Pizzas: 27
Step-by-step explanation:
L = # of large Pizzas
M = # of medium Pizzas
S = # of small Pizzas
Amount:
L = 4M - 2
S = 3M + 3
Cost:
21L + (I'm assuming you meant 14) 14M + 7S = 931
Plus in the Amounts to the Cost:
21(4M - 2) + 14M + 7(3M + 3) = 931
84M - 42 + 14M + 21M +21 = 931
Combine like terms:
119M - 21 = 931
Isolate the Variable:
119M - 21 + 21 = 931 + 21
119M = 952
119M/119 = 952/119
M = 8
Plug it into the Amount equations:
Large: L = 4(8) - 2
L = 32 - 2
L = 30
Small: S = 3M + 3
S = 3(8) + 3
S = 24 + 3
S = 27
Check your work (plug the values into Cost.):
21(30) + 14(8) + 7(27) = 931
630 + 112 + 189 = 931
931 = 931
The number of medium pizzas ordered was 10. Hence, based on the given relationships, the number of large pizzas was 38 and the number of small pizzas was 33.
Explanation:To solve this problem, really, we are using three algebraic expressions that represent the total cost, the relationship between the large and medium pizzas, and the relationship between the small and medium pizzas.
We can define M as the number of medium pizzas, L as the number of large pizzas, and S as the number of small pizzas. We can then set up the following equations based on the problem:
$21L + $14M + $7S = $931L = 4M - 2S = 3M + 3We can substitute equations 2 and 3 into equation 1 to get a single equation in terms of M:
$21(4M-2) + $14M + $7(3M+3) = $931
Which simplifies to:
93M = 931
Then, M=10, hence, the number of medium pizzas is 10, number of large pizzas (4M-2) is 38, and the number of small pizzas (3M+3) is 33.
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What is the solution to this equation?
8x - 5 (x-3) = 18
Answer:
x=1
Step-by-step explanation:
We distribute the negative 5 to x minus three to get 8x-5x+15=18. Then, we cancel out the 15 by subtracting it from both sides. This leaves us with 8x-5x=3. When we subtract, we get 3x=3, and when we divide both sides by 3, we get x=1. Hope this helps :)
Why is money as a store of value useful for business owners?
Answer:
B
Step-by-step explanation:
it is a simple exchange for goods and services because, is stores value for later use.
there is a bag filled with 3 blue, 4 red and 5 green marbles. a marble is taken at random. what is the probability of exactly 1 red?
Answer:
P 1 red) = 1/3
Step-by-step explanation:
We have 12 marbles (3+4+5)
P(red) = red marbles/ total marbles
= 4/12 = 1/3
Answer:
4 / 12 or 1/3
Step-by-step explanation:
The total is 3 blue, 4 red and 5 green marbles which is 12 marbles altogether.
There is exactly 4 marbles out of the 12 marbles that are red so the probability of choosing a red is 4 / 12 or 1/3
Thank you guys soo much
Answer:
a. 64 tickets.
b. $11.
Step-by-step explanation:
a.[tex]y[/tex] is given as [tex]37[/tex], and the question is asking for the value of [tex]x[/tex].
Solve this equation with respect to [tex]x[/tex].
[tex]0.50x + 5.00 = 37[/tex].
Subtract 5.00 from both sides of this equation:
[tex]0.50x = 32[/tex].
[tex]\displaystyle x= \frac{32}{0.50} = 64[/tex].
In other words, 64 tickets were purchased.
b.[tex]x = 12[/tex], and the question is asking for the value of [tex]y[/tex].
Replace [tex]x[/tex] with 12 and evaluate the expression [tex]y = 0.50x + 5.00[/tex] for [tex]y[/tex].
[tex]y = 0.50\times 12 + 5.00 = 11.00[/tex].
In other words, $11.00 were spent.
Please help asap
Explain your answer
[tex]12=2\cdot7+1\\12=15[/tex]
[tex]LHS\not=RHS[/tex] so no, it isn't on the line.
Can someone please help me out with this question??
Answer:
see explanation
Step-by-step explanation:
The error is in Step 1, by not adding 2 on the left side, that is
Given
7.7 = w - 2 ( add 2 to both sides )
7.7 + 2 = w - 2 + 2
9.7 = w
R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)} Select all numbers that are in the domain. -3 -2 -1 0 1 2
Answer:
[tex]-3,\ -1,\ 1[/tex]
Step-by-step explanation:
You are given the relation
[tex]R=\{(-3,-2),\ (-3,0),\ (-1,2),\ (1,2)\}[/tex]
The domain of the relation are all possible inputs and the range of the relation are all possible outputs. In your case,
inputs are: [tex]-3,\ -1,\ 1;[/tex]outputs are: [tex]-2,\ 0,\ 2.[/tex]So,
the domain is [tex]-3,\ -1,\ 1;[/tex]the range is [tex]-2,\ 0, 2.[/tex]Answer:
-3, -1, and 1
Step-by-step explanation:
hope that helps :)
A line passes through (3, -2) and (6,2). Write an equation for the line in point-slope form.
Rewrite the equation in standard form using integers.
Answer:
4x - 3y -18 = 0 or y = 4x/3 - 6
Step-by-step explanation:
We will have to find the slope of the line first
The formula for slope:
[tex]m =\frac{y_{2}- y_{1} }{x_{2} -x_{1} } \\m= \frac{-2-2}{3-6}\\ =\frac{-4}{-3}\\ =\frac{4}{3}[/tex]
The standard form of equation of a line is:
y = mx + b
We know m,
So the equation will be:
[tex]y= \frac{4}{3}x+b[/tex]
We have to find the value of b, for that we will put any one of the point in the equation
So, putting (6,2)
2 = 4/3 * 6 + b
2 = 8 +b
b = -6
Putting the value of m and b in the standard form of equation of line,
[tex]y = mx + b\\y = \frac{4}{3}x+(-6)\\y = \frac{4}{3} x - 6\\Multiplying\ both\ sides\ by\ 3\\3y = 4x - 18\\4x - 3y -18 = 0[/tex] ..