Draw a line through each point using the given slope. What do you notice about the two lines?
Answers
The two lines are parallel with equal slopes, will never intersect, and have different y-intercepts, showing a constant vertical distance.
To draw a line through each point using the given slope, we will use the slope-point form of a line equation, which is [tex]\( y - y_1 = m(x - x_1) \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( (x_1, y_1) \)[/tex] is the point through which the line passes.
The slope given is [tex]\( \frac{1}{2} \)[/tex]. We have two points, [tex]\( (-2, 1) \)[/tex] and [tex]\( (4, -2) \)[/tex]. Let's calculate the equation of the line for each point.
For the point [tex]\( (-2, 1) \)[/tex]:
[tex]\[ y - 1 = \frac{1}{2}(x - (-2)) \][/tex]
[tex]\[ y - 1 = \frac{1}{2}(x + 2) \][/tex]
[tex]\[ y = \frac{1}{2}x + 2 \cdot \frac{1}{2} + 1 \][/tex]
[tex]\[ y = \frac{1}{2}x + 2 \][/tex]
For the point [tex]\( (4, -2) \)[/tex]:
[tex]\[ y - (-2) = \frac{1}{2}(x - 4) \][/tex]
[tex]\[ y + 2 = \frac{1}{2}x - 4 \cdot \frac{1}{2} \][/tex]
[tex]\[ y = \frac{1}{2}x - 2 - 2 \][/tex]
[tex]\[ y = \frac{1}{2}x - 4 \][/tex]
Now we have the equations for both lines, plot them on the graph to show the relationship between them. Let's proceed with plotting these lines.
(GRAPH IS GIVEN BELOW)
The graph shows two lines:
1. The red line passes through the point [tex]\((-2, 1)\)[/tex] and has a slope of [tex]\(\frac{1}{2}\)[/tex]. Its equation is [tex]\(y = \frac{1}{2}x + 2\)[/tex].
2. The blue line passes through the point [tex]\((4, -2)\)[/tex] and also has a slope of [tex]\(\frac{1}{2}\)[/tex]. Its equation is [tex]\(y = \frac{1}{2}x - 4\)[/tex].
Observing the two lines on the graph, you can notice the following points:
1. Both lines have the same slope of [tex]\(\frac{1}{2}\)[/tex], which means they are parallel to each other.
2. Because they are parallel, the two lines will never intersect each other.
3. The lines have different y-intercepts, which is consistent with parallel lines that are not coincident.
4. The difference in the y-intercepts 2 for the first line and [tex]\(-4\)[/tex] for the second line) corresponds to the vertical distance between the two lines.
Related Questions
what theorems/ info about proportional parts in triangle and parallel lines should I use to find the missing length of a triangle? how should I set up an equation? Please explain with details, I will be so grateful.
Answers
So first, yes, you find the missing length (piece plus piece equals whole part) and proportional, you just visualize ( like let's say there are two similar shapes that are smilier : ABCD~ FGHJ and let's say AB is 3 FG is 9 , so i would say 3/9 . And for CD is ,..let's say 8 and HJ is 16, so 8/16. So basically:
3 = 9
-- --
8 16 <--- that's how you set up proportional
i hope you understand , and if not, feel free to message me!
Have a beautiful day
I NEED HELP WITH 2 QUESTIONS I WILL MAKE SOME THAT GETS THEM CORRECT THE BRAINIEST, THANKS, AND RATE
Peter earned $180 working at a store during the summer months. He bought 4 books worth $12 each from his earnings at the store. How much money was left after he bought the books?
A$33
B$42
C$132
D$228
Tom bought 5 t-shirts from a store. After he bought the t-shirts, his account balance showed a change of –$65.25. What would have been the change to Tom's account balance had he only bought 1 t-shirt from the store?
A$13.05
B–$13.05
C$13.50
D–$13.50
Answers
4 books of 12 dollar each will be 4 x 12= 48 dollars
180 - 48 = 132 dollars is left
2. tom bought 5 t shirts. he didnt pay any money so we assume that he paid 0 dollars.
the price of one shirt will be -65.25 dollars / 5
which will give -13.05 dollars
Answer:
1. The correct answer choice is C $132.
2. The correct answer choice is B -$13.05
Step-by-step explanation:
1. 12 x 4 = 48.
180 - 48 = 132
2. -65.25/5 = -13.05
Yes, I know this is already answer.
Also, I took the test :)
Have a good day!
Write addition fact that helps you to solve 12-4
Answers
How many numbers from 1 to 100 can be divided by 2 with none leftover.
Answers
3/4-1/4=
1/2+3/8=
6 1/2-2 1/2=
3 1/2-1 1/8=
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2) 7/8
3) 4
4) 19/8 = 2 3/8
_____________________
Explanation:
_____________________
3/4 − 1/4 = 2/4 = 1/2 ; or, ½ .
________________________________________________
2) Answer: ⅝ .
________________________
Explanation:
______________
1/2 + 1/8 = (1*4)/(2*4) + 1/8 = 4/8 + 1/8 = 5/8 ; or, ⅝ .
________________________________________________
3) Answer: 4 .
____________
Explanation:
______________
6 ½ − 2 ½ = 4 . (or; 6.5 − 2.5 = 4.0 = 4 .).
_______________________________________________
4) Answer: 2 ⅜ .
_________________
Explanation:
_________________
3 1/2 − 1 1/8 = ?
_______________
→ 1/2 = (1*4)/(2*4) = 4/8; → So rewrite: "3 1/2" as: "3 4/8"; and rewrite the problem:
___________________________________________
→ 3 4/8 − 1 1/8 = 2 3/8 ; or, 2 ⅜ .
___________________________________________
jamal works in a city and sometimes takes a taxi to work. The taxicabs charge $1.50 for the first 1/5 mile and $0.25 for each additional 1/5 mile. Jamal has only $3.75 in his pocket. What is the maximum distance he can travel by taxi if he does not tip the driver?
Can someone help with this question please?
Answers
He pays 1.50 for the first mile so take 1.50 from the 3.75 and you will get 2.25$.
So take the 2.25 and divide it by how much he will have to pay for each mile .So 2.25/0.25 and you get 0.09 .But you can also just take 1.50 away from 3.75 and get 2.25 the count how many quarters is in 2.25. but you will have to multiply 9 by 1/5 which is 1.8 miles .Its that or 9
Find the quotient of 1.2 divided by 251.2 show your work
Answers
After divide, the quotient of 1.2 divided by 251.2 is 0.004777.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
⇒ 1.2 divided by 251.2
Solve this as;
⇒ 1.2 ÷ 251.2
⇒ 0.004777
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A CD player is on sale for $90 at an electronics store. If the original price was $125, what was the percent of discount
Answers
Find the amount of discount : $125 - $90 = $35
Divide by the original price : $35/125 = 0.28
Change in to percentage : 0.28 x 100 = 28%
Therefore the percentage discount is 28% off
:)
Triangle XYZ is similar to triangle RST what is the perimeter of triangle RST
Answers
The perimeter of triangle RST is B) 56.25 units. Therefore, the correct answer is B) 56.25 units.
The perimeter of a triangle is the sum of the lengths of its sides.
Since triangle XYZ is similar to triangle RST, the ratio of the corresponding sides of the two triangles is the same.
Therefore, we can set up the following proportion:
XY / XZ = RS / RT
Substituting the known values, we get:
15 / 4 = RS / RT
Multiplying both sides by RT, we get:
15 = RS * RT
We also know that the sum of the angles in a triangle is 180 degrees. Therefore, we can set up the following equation:
90 + ∠RST + ∠SRT = 180
Substituting the fact that triangle XYZ is similar to triangle RST, we get:
90 + ∠XYZ + ∠XZY = 180
Substituting the known values, we get:
90 + 30 + 60 = 180
Therefore, ∠RST = 60 degrees.
Now that we know the lengths of two sides of triangle RST and the measure of one angle, we can use the law of cosines to find the length of the third side:
RT^2 = RS^2 + ST^2 - 2 * RS * ST * cos(∠RST)
Substituting the known values, we get:
RT^2 = 15^2 + ST^2 - 2 * 15 * ST * cos(60 degrees)
Simplifying, we get:
RT^2 = 225 + ST^2 - 15ST
We also know that the perimeter of triangle RST is equal to the sum of the lengths of its sides:
Perimeter = RS + RT + ST
Substituting the fact that triangle XYZ is similar to triangle RST, we get:
Perimeter = 15 + RT + ST
Now that we know the length of RT and the fact that the perimeter of triangle RST is equal to the sum of the lengths of its sides, we can substitute these values into the equation for the perimeter to find the length of the third side, ST:
Perimeter = 15 + RT + ST
ST = Perimeter - 15 - RT
ST = 56.25 - 15 - 37.5
ST = 3.75
Therefore, the perimeter of triangle RST is:
Perimeter = RS + RT + ST
Perimeter = 15 + 37.5 + 3.75
Perimeter = 56.25
Therefore, the correct answer is B) 56.25 units.
for such more question on perimeter
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Question
Triangle XYZ is similar to triangle RST.
Side lengths:
XY = 15 units
XZ = 4 units
YZ = 6 units
Angle measures:
∠X = 90°
What is the perimeter of triangle RST?
A) 45 units
B) 56.25 units
C) 37.5 units
D) 15 units
a go carts too speed is 607200 feet per hour. what is the speed in mph?
Answers
Admission to a car show costs $5 for each ticket. After selling only 20 tickets, they decided to lower the price to $3 each. If they raise $217 ,how many tickets did they sell in all?
Answers
If r = 5 units and x = 7 units, then what is the volume of the cylinder shown above?
A.
175 cubic units
B.
35 cubic units
C.
120 cubic units
D.
700 cubic units
Answers
Answer:
175 cubic units
Have a good day.
One serving of milk has 120 calories. If one serving is equal to one cup how many calories are in one fluid ounce. 1 Cup = 1 fluid ounce
A. 10
B. 12
C. 16
D. 15
Answers
nadia has 4 sheets of stickers there are 8 stickers on each sheet .she wrote this number sentence to represent the totel number of stickers
Answers
Answer:32
Step-by-step explanation:
This question requires multiplying.
Think of 4 sheets as 4 groups. If there are 8 stickers in the first group, we still have 8, then we will add 8 to the second group. We will have 16. Next we will add 8 to third the third group, 24, and third to the fourth group which will give us 32. 8,16,24,32.
Our equation will be 8×4=32
What is the approximate percent decrease when a fish count goes down from 850 to 500?
Answers
Answer:
About 40%
Step-by-step explanation:
It would normally be 41.--% But rounded is the approximate percent so it would be 40%. I hope this helps you! :)
Answer: 41%
Step-by-step explanation:
The change in fish count = [tex]850-500=350[/tex]
The percent decrease when a fish count goes down from 850 to 500 is given by :-
[tex]\text{Percent decrease}=\frac{\text{Change in fish count}}{\text{Previous fish count}}\times100\\\\\Rightarrow\text{Percent decrease}=\frac{350}{850}\times100\\\\\Rightarrow\text{Percent decrease}=41.176470588\%\approx41\%[/tex]
Hence, the approximate percent decrease when a fish count goes down from 850 to 500= 41%
How do i solve? 2/3h = -9
Answers
therefore
2 = -27h
h = -27/ 2
yeah
how many tenths are there in 4/5
Answers
4/5 = 8/10
You multiple nominator and denominator by 2
Mr. Rivas bought a can paint. he used 3/8 of it to paint a bookshelf. he used 1/4 of it to paint a wagon. he used some of it to paint a birdhouse and has 1/8 of the paint left. how much paint did he use for he birdhouse
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38 1/4 divided by 4 1/2
Answers
38 1/4 = 153/4 and 4 1/2= 9/2
153/4 divided by 9/2
153/4 x 2/9
= 17/2 or 8 1/2
5 1/3-w= 4
These problems confuse me so much.
Answers
Please help it's due tommorow!! I need answers for questions 29-40
Answers
How do you write this equation "at a concert,you purchase 3 T-shirts and a concert program for a total cost of $90.The program cost $15 and the T-shirts all cost the same.Write and solve an equation to find the cost of one T-shirt."
Answers
Hank cut a cake into 12 equal pieces. He ate 2/12 pieces. He has 10/12 of the cake left to serve on plates. What part of the cake did he put on each plate.
Answers
Trampoline Park has an admission fee, plus an hourly fee of $4.50. Determine the admission fee that the trampoline park charges. What is the initial value?
Answers
The initial value of a function is when x = 0. The initial value of the Trampoline Park is $5.00
Given that:
[tex](x_1,y_1) \to (3,18.5)[/tex]
[tex]m = 4.50[/tex] ---- the rates
The equation is calculated using:
[tex]y = m(x - x_1) + y_1[/tex]
So, we have:
[tex]y = 4.50(x - 3) + 18.5[/tex]
Open bracket
[tex]y = 4.50x - 13.5 + 18.5[/tex]
[tex]y = 4.50x + 5.00[/tex]
The initial value is when [tex]x=0[/tex]
So, we have:
[tex]y = 4.50 \times 0 + 5.00[/tex]
[tex]y = 5.00[/tex]
Hence, the initial value is $5.00
Read about linear functions at:
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Solve for P.
4p = 1/2
Answers
This is very simple if you think about it.
To solve here is what you need to do:
4p = 1/2
Divide both sides by 4 -
4p/4 = 1/2/4
p = 1/8
This of course cannot be simplified any lower than what it is because the numerator is a 1. When it is a 1 it cannot be smaller. (Note that a fraction cannot have a decimal number as its numerator OR denominator.)
Hope this helps!
Answer:
1/8
Step-by-step explanation:
You need to find P not 4p so you divide 4p by 4 to get P and by doing this you have to divide the other side too. so now you got 4p/4 = 1/2/4 which = p=1/8
estimate 4 divided by 1165
Answers
Hope this helps!!
what is the meaning of term
Answers
of what some one is say
your friend has owned a dog for 9 years. This is one year less than twice as long as he has owned a cat. How long has your friend owned a cat? write and solve an eqaution
Answers
(9x2)-1=x
Karen is writing a word problem that can be represented by the equation 2x + 3 = 13.
A bucket weights 2 grams and balls are put into it that each weight 3 grams. The total weight of the bucket and balls is 13 grams. How many balls are in the bucket?
Does her word problem fit the equation? Justify your response.
Answers
because the bucket weighs two grams, and the balls which are represented by (x) each weigh 3 grams.
I WILL PICK THE BRAINLIEST FOR WHOEVER HAS THE CORRECT ANSWER!
Answers
2.150
Prizes you need 1 for every 10 entrees so the difference is 1prize per 10Entrees
150 entrees is what the graph needs to show and /10= 15