Answers
Answer: [tex]x^{\frac{2}{3} }[/tex]
Step-by-step explanation:
We have several properties of exponents in use here. The two that are used are:
[tex](x^{a})(x^{b}) = x^{a + b}[/tex] (Exponents with the same base that are being multiplied together can have the exponents added)
[tex](x^{a})^{b} = x^{(a)(b)}[/tex] (A base raised to a power, and then raised to another power means that you can multiply the exponents to get the same result as doing inside operations and then outside operations)
Let's apply it!
First, let's simplify what's inside the parenthesis.
[tex]x^{\frac{4}{3} } x^{\frac{2}{3} }[/tex] (Remember, they have the same base of "x", so we can add the exponents)
[tex]x^{\frac{4}{3} + \frac{2}{3} }[/tex] = [tex]x^{\frac{6}{3} }[/tex] = [tex]x^{2}[/tex]
Now we have [tex](x^{2})^{\frac{1}{3} }[/tex]. Let's use the second rule.
[tex](x^{2})^{\frac{1}{3} }[/tex] = [tex]x^{\frac{2}{3} }[/tex]
Hope this helps! :^)
Answer:
B
Step-by-step explanation:
Just took the test
Related Questions
What is the slope-intercept form of the equation of the line that passes through the points (-3, 2) and (1, 5)?
A) y=3/4 x− 7/4
B) y=3/4 x- 9/2
C) y=3/4 x+ 7/2
D) y=3/4 x + 17/4
Answers
[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{5}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{5-2}{1-(-3)}\implies \cfrac{3}{1+3}\implies \cfrac{3}{4}[/tex]
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-2=\cfrac{3}{4}[x-(-3)] \implies y-2=\cfrac{3}{4}(x+3) \\\\\\ y-2=\cfrac{3}{4}x+\cfrac{9}{4}\implies y=\cfrac{3}{4}x+\cfrac{9}{4}+2\implies y=\cfrac{3}{4}x+\cfrac{17}{4}[/tex]
Please help me with this problem ASAP!!!!
Answers
For this case we have a function of the form [tex]y = f (x)[/tex]
They ask us to find the value of the function when[tex]x = 2[/tex], that is, [tex]f (2).[/tex]
If we look at the figure, and we mark x = 2 in the graph, we obtain a value of[tex]y = 4[/tex]
So, we have that the function has a value of 4 when[tex]x = 2[/tex]
Answer:
Option C
The rectangular wall below is painted in 15 minutes. How many square feet per minute were painted?
Answers
The rectangular wall that is painted in 15 minute. 6.4 square feet area is painted per minute.
What is rectangle?A rectangle is a part of a quadrilateral, whose sides are parallel to each other and equal.
Given that,
The length of the rectangular wall = 12 ft.
The width of the rectangular wall = 8 ft.
The area of rectangle = 12 x 8 = 96 square feet.
Since, in 15 minutes, the rectangular wall is painted.
To find the area that painted in one minute,
Use ratio property,
15 minutes = 96 square feet painted,
1 minute = 96 / 15 square feet painted.
1 minute = 6.4 square feet.
6.4 square feet painted in 1 minute.
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Fracisco's game involves 3 green, 2 yellow, 4 red, and 3 black marbles. If he randomly draws three marbles from the
bag, without replacement, what is the probability that he will draw yellow, and then red, and then black?
A)1/192
B)1/72
C)3/220
D)1/55
Answers
Answer:1/55
Step-by-step explanation:
Answer: The answer is 1/55
Step-by-step explanation: because i got it right on edge. Can you mark brainliest?
Type the correct answer in each box. Use numerals instead of words.
You reflect triangle PQR, with coordinates P(-4, -4), Q(-1, -3), and R(-3, -1), across the x-axis, across the y-axis, and across the x-axis again to form triangle P′Q′R′.
After these reflections, the coordinates of P′ will be (,
Answers
Answer:
After these reflections, the coordinates of P′ will be (4 , -4)
Step-by-step explanation:
* Lets revise some transformation
- If point (x , y) reflected across the x-axis
∴ Its image is (x , -y)
- If point (x , y) reflected across the y-axis
∴ Its image is (-x , y)
* Lets solve the problem
- The triangle PQR with coordinates P(-4, -4), Q(-1, -3), and R(-3, -1)
- The triangle is reflected across the x-axis
∵ Δ PQR is reflected across the x-axis
∴ All y-coordinates of the vertices P, Q , R reversed their signs
∴ The new points will be (-4 , 4) , (-1 , 3) , (-3 , 1)
- The new vertices will reflected across the y-axis
∴ All x-coordinates of the new vertices reversed their signs
∴ The new points will be (4 , 4) , (1 , 3) , (3 , 1)
- The new vertices will reflected across the x-axis to form Δ P'Q'R'
∴ All y-coordinates of the new vertices reversed their signs
∴ P' = (4 , -4) , Q' = (1 , -3) , R' = (3 , -1)
* After these reflections, the coordinates of P′ will be (4 , -4)
Final answer:
After reflecting triangle PQR across the x-axis, then the y-axis, and the x-axis again, point P' will have coordinates (4, -4).
Explanation:
Reflecting a triangle across an axis involves flipping the triangle over that axis. Each reflection inverses the corresponding coordinate (x or y) of each vertex of the triangle, while the other coordinate remains the same. Starting with the first reflection across the x-axis, the y-coordinate of each point negates, but the x-coordinate remains unchanged. The second reflection is across the y-axis, which negates the x-coordinate and keeps the y-coordinate (already negated from the first reflection) the same. The third reflection across the x-axis negates the y-coordinate again, effectively returning it to its original value before the first reflection. So for point P(-4, -4), after these reflections, the new coordinates for P' will be (4, -4).
If f(x)=4x+3 and g(x)= the square root of x-9, which is true? 2 is in the domain of f of g or 2 is not in the domain of f of g?
Answers
Answer:
2 is not in the domain of f of g
Step-by-step explanation:
* Lets revise at first the meaning of f of g (composite function)
- A composite function is a function that depends on another function
- A composite function is created when one function is substituted into
another function
- Example:
# f(g(x)) is the composite function that is formed when g(x) is
substituted for x in f(x).
- In the composition (f ο g)(x), the domain of f becomes g(x)
* Now lets solve the problem
∵ f(x) = 4x + 3
∵ g(x) = √(x - 9)
- Lets find f(g(x)), by replacing x in f by g(x)
∴ f(g(x)) = f(√(x - 9)) = 4[√(x - 9)] + 3
∴ f(g(x)) = 4√(x - 9) + 3
∵ The domain of f is g(x)
- The domain of the function is the values of x which make the
function defined
∵ There is no square root for negative values
∴ x - 9 must be greater than or equal zero
∵ x - 9 ≥ 0 ⇒ add 9 for both sides
∴ x ≥ 9
∴ The domain of f of g is all the real numbers greater than or equal 9
∴ The domain = {x I x ≥ 9}
∵ 2 is smaller than 9
∴ 2 is not in the domain of f of g
You have $20. Suppose you make x dollars in tips tomorrow at work. Which inequality must be true for you to have enough money to buy a pair of jeans after work?
Answers
Answer:
B) x +20 is greater than or less to 45
Step-by-step explanation:
Answer:
x + 20 ≥ 45
Step-by-step explanation:
You currently have : $20
You will earn : $x
Tomorrow you will end up with (20 + x) dollars
the pair of jeans cost $45, in order to afford the jeans, the amount of money that you will need must be equal or more than $45
Hence,
Money you will have tomorrow ≥ 45
or
x + 20 ≥ 45 (Answer)
eighteen million, one hundred two thousand, seven hundred eighty-three as a whole number?
Answers
Answer:
18,102,783
Step-by-step explanation:
Write as an algebraic expression and then simplify if possible The distance traveled by a train in three hours with a constant speed of r miles per hour.
Answers
Answer:
Distance = 3r
Step-by-step explanation:
We are to write an algebraic expression and then simplify it for the given situation:
The distance traveled by a train in three hours with a constant speed of r miles per hour.
We know the formula of distance linking the speed and the time.
Distance = speed × time
Substituting the given values to get:
Distance = r × 3
Distance = 3r
In the summer a large pool evaporates water at 15% per day. If the pool starts out with 25,700 gallons of water, which function models the pool’s loss of water?
Answers
Answer:
[tex]y=25,700(0.85)^{x}[/tex]
Step-by-step explanation:
we know that
In this problem we have a exponential function of the form
[tex]y=a(b)^{x}[/tex]
where
y ----> represent the pool’s loss of water
x ----> the number of days
a is the initial value
a=25,700 gal
b ----> is the base
r=15%=15/100=0.15
b=(1-r)=1-0.15=0.85
The function is equal to
[tex]y=25,700(0.85)^{x}[/tex]
if f(x)=3x-1 and g(x)=x+2,find (f-g)(x)
Answers
Answer:
[tex]\large\boxed{(f-g)(x)=2x-3}[/tex]
Step-by-step explanation:
[tex](f-g)(x)=f(x)-g(x)\\\\f(x)=3x-1,\ g(x)=x+2\\\\\text{substitute:}\\\\(f-g)(x)=(3x-1)-(x+2)\\\\=3x-1-x-2\qquad\text{combine like terms}\\\\=(3x-x)+(-1-2)\\\\=2x-3[/tex]
A cable company claims that the average household pays $78 a month for a basic cable plan, but it could differ by as much as $20. Write an absolute value inequality to determine the range of basic cable plan costs with this cable company.
A. |x − 78| ≥ 20
B. |x − 20| ≥ 78
C. |x − 20| ≤ 78
D. |x − 78| ≤ 20
Answers
Answer:
D. |x − 78| ≤ 20
Step-by-step explanation:
Given,
The monthly charges for a basic cable plan = $ 78,
Also, it could differ by as much as $20,
So, the maximum charges = $(78 + 20) ,
And, the minimum charges = $(78 - 20),
Let x represents the monthly charges ( in dollars ),
78 - 20 ≤ x ≤ 78 + 20
⇒ 78 - 20 ≤ x and x ≤ 78 + 20
⇒ -20 ≤ x -78 and x-78 ≤ 20
⇒ 20 ≥ -(x-78) and x-78 ≤ 20 ( ∵ a > b ⇒ -a < -b )
⇒ |x-78| ≤ 20
Which is the required absolute value inequality to determine the range of basic cable plan costs,
Option 'D' is correct.
How to write (3+4i)+(8+2i) as a complex number in standard form
Answers
Answer:
Answer is 11+6i
Step-by-step explanation:
You just have to add imaginary part together and the real part. The answer will be 11+6i
Answer: 11+6i
Step-by-step explanation:
Kathy distributes jelly beans among her friends. Alia gets 4^2 fewer jelly beans than Kelly, who gets 3^3 jelly beans. How many jelly beans does Alia get? A. 4^2 − 3^3 B. 3^3 + 4^2 C. 4 − 3^3 D. 3^3 − 4^2 E. 3^2 − 4^3
Answers
Kelly got 3^3 (27) while Alia got 4^2 (16) less than her. When you put it together you get 3^3 - 4^2
Answer:
Option D. Alia gets 3³ - 4² = 11 jelly beans.
Step-by-step explanation:
Kathy gives Kelly 3³ jelly beans.
Kathy gives Alia 4² fewer jelly beans than Kelly. This means that Alia gets the number of jelly beans obtained by Kelly decreased by 4².
To summarize:
#Kelly = 3³ = 27
#Alia = #Kelly - 4² = 3³ - 4² = 27 - 16 = 11
Then, option D is correct.
the lines shown below are parallel. if the green line has a slope of -1, what is the slope of the red line
Answers
Answer: -1 is the slope of the red line,
Step-by-step explanation: The slope of parallel lines are always the same. Hope this helps!
Answer:
the slope would be -1
Step-by-step explanation:
PLEASE HELP!
Drag the tiles to the correct boxes to complete the pairs.
Match the rational expressions to their rewritten forms.
Just Answer Please!
Answers
Answer:
1. [tex]\frac{x^2+4x-7}{x-1}[/tex]
2. [tex]\frac{x^2-2x+7}{x-1}[/tex]
3. [tex]\frac{2x^2-x-7}{x-1}[/tex]
4. [tex]\frac{2x^2-3x+7}{x-1}[/tex]
Step-by-step explanation:
1. [tex](x+5) + \frac{-2}{x-1}[/tex]
Taking LCM
[tex]=\frac{(x-1)(x+5)+(-2)}{x-1}\\ Solving:\\=frac{x(x+5)-1(x+5)-2}{x-1} \\=frac{x^2+5x-1x-5-2}{x-1} \\Adding\,\,like\,\,terms:\\=\frac{x^2+4x-7}{x-1}[/tex]
2. [tex]x-1 +\frac{6}{x-1}[/tex]
Taking LCM and solving
[tex]=\frac{(x-1)(x-1)+6}{x-1}\\=\frac{(x(x-1)-1(x-1)+6}{x-1}\\=\frac{x^2-1x-1x+1+6}{x-1}\\Adding\,\,like\,\,terms:\\=\frac{x^2-2x+7}{x-1}[/tex]
3. [tex](2x+1)+\frac{-6}{x-1}[/tex]
Taking LCM and solving:
[tex]=\frac{(2x+1)(x-1)-6}{x-1} \\=\frac{2x(x-1)+1(x-1)-6}{x-1} \\=\frac{2x^2-2x+1x-1-6}{x-1}\\Adding\,\,like\,\,terms:\\=\frac{2x^2-x-7}{x-1}[/tex]
4. [tex](2x-1)+\frac{6}{x-1}[/tex]
Taking LCM and solving:
[tex]=\frac{(2x-1)(x-1)+6}{x-1} \\=\frac{2x(x-1)-1(x-1)-6}{x-1} \\=\frac{2x^2-2x-1x+1+6}{x-1}\\Adding\,\,like\,\,terms:\\=\frac{2x^2-3x+7}{x-1}[/tex]
Answer:
I'm pretty sure that is correct.
Step-by-step explanation:
which of the following best describes an altitude of a three-dimensional object?
Answers
Answer:
Option C
Step-by-step explanation:
we know that
The altitude of a three-dimensional object is equal to the height of the object, is the perpendicular distance of the base to the other base or the perpendicular distance of the base to the apex of the object
therefore
A segment that is perpendicular to the planes containing the two bases
The statement which best describes an altitude of a three-dimensional object is: C. a segment that is perpendicular to the planes containing the two bases.
What is altitude?Altitude is also referred to as an elevation and it can be defined as the vertical distance (height) above the surface of a plane.
In Geometry, the altitude of a three-dimensional object is characterized by the following:
It's equal to the height of the object.It's the perpendicular distance between two bases.It's the perpendicular distance of a base to the ap-ex of an object.Read more on altitude here: https://brainly.com/question/3946367
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which expression is equivalent to...
Answers
Answer:
C
Step-by-step explanation:
Use exponents property:
[tex]\dfrac{x^a}{x^b}=x^{a-b}[/tex]
1. Note that
[tex]\dfrac{x^7}{x^{11}}=x^{7-11}=x^{-4}=\dfrac{1}{x^4}[/tex]
and
[tex]\dfrac{y^6}{y^8}=y^{6-8}=y^{-2}=\dfrac{1}{y^2}[/tex]
2. Now
[tex]\sqrt{\dfrac{55x^7y^6}{11x^{11}y^8}}=\sqrt{\dfrac{5}{x^4y^2}}=\dfrac{\sqrt{5}}{\sqrt{x^4}\sqrt{y^2}}=\dfrac{\sqrt{5}}{x^2y}[/tex]
because [tex]x>0,\ y>0[/tex]
How do you work out 15 divided by 25
Answers
Answer:
Step-by-step explanation:
15/25. Divide both sides by a common number which is 5 3/5 is the final answer.
The result of the given mathematical expression is [tex]\frac{3}{5}[/tex] or 0.6.
What is a mathematical expression?"A mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context."
Given mathematical expression is
= (15 ÷ 25)
[tex]= \frac{15}{25}\\= \frac{3}{5}\\= 0.6[/tex]
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Paul plans to put concrete on a rectangular portion of a driveway. The portion is 12 feet long and 6 inches high. The price of the concrete is $98.00 per cubic yard. The total cost of the concrete Paul needs is $108.89. What is the width of the driveway in feet which Paul plans to put concrete?
Answers
Answer: 5 ft
Step-by-step explanation:
Step 1: Find the volume of the driveway (in cubic yds)
[tex]\$ 108.89\div\dfrac{\$98}{yds^3}=\$ 108.89\times\dfrac{yds^3}{\$98}=\boxed{\dfrac{10}{9}yds^3}[/tex]
Step 2: Use the Volume formula (V = length × width × heighth) to find w
(convert each measurement into yds)
[tex]V=l\times w\times h\\\\\dfrac{10}{9}yds^3=12ft\bigg(\dfrac{1yd}{3ft}\bigg)\times w\times 6in\bigg(\dfrac{1ft}{12in}\bigg)\bigg(\dfrac{1yd}{3ft}\bigg)\\\\\\\dfrac{10}{9}yds^3=4yds\times w\times \dfrac{1}{6}yds\\\\\\\dfrac{10}{9}yds^3=\dfrac{2}{3}yds^2\times w\\\\\\\dfrac{3}{2yds^2}\times \dfrac{10}{9}yds^3=w\\\\\\\dfrac{5}{3}yds=w\\\\\\\dfrac{5}{3}yds\times\dfrac{3ft}{1yd}=w\\\\\\\large\boxed{5 ft=w}[/tex]
A student factors 10x^2+3x-27 to the following
A. The expression is equivalent, and it is completely factored
Answers
At the beginning of year 1, Jonah invests $300 at an annual
compound interest rate of 4%. He makes no deposits to or
withdrawals from the account.
Which explicit formula can be used to find the account's
balance at the beginning of year 6?
Answers
The explicit formula that can be used to find the account's balance at the beginning of year 6 is B = P(1 + r/n)^(nt), which gives the value as [tex]300(1.04)^6[/tex]
Explanation:The explicit formula that can be used to find the account's balance at the beginning of year 6 is:
[tex]B = P(1 + r/n)^(nt)[/tex]
Where:
B is the balance after a certain number of yearsP is the principal amount (initial investment)r is the annual interest rate (as a decimal)n is the number of times that interest is compounded per yeart is the number of yearsIn this case, Jonah's initial investment is $300, the annual interest rate is 4%, interest is compounded annually (n = 1), and the number of years is 6 (t = 6). Plugging these values into the formula:
[tex]B = 300(1 + 0.04/1)^(1*6)[/tex]
[tex]B = 300(1 + 0.04)^6[/tex]
[tex]B = 300(1.04)^6[/tex]
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Help answer this please
Answers
Answer:
B
Step-by-step explanation:
translation means to transcribe or change from on language/definition/understanding to another.
Solve each problem by writing and solving an equation.
For his son’s birthday party, Mr. Mori bought four equally-priced pizzas and a $3 bag of potato chips. If he spent $39, find the cost of each pizza.
Question 2 options:
Answers
Answer:
Each pizza costs for $9.
Step-by-step explanation:
We are given that Mr. Mori bought four equally-priced pizzas and a $3 bag of potato chips.
Given that he spent a total $39, we are to find the cost of each pizza.
This can be represented by an equation:
[tex]4x+3=39[/tex]
Solving it to find x.
[tex]4x=39-3[/tex]
[tex]4x=36[/tex]
[tex]x=\frac{36}{4}[/tex]
x = 9
Therefore, the cost of each pizza is $9.
Answer:
C.X=9
Step-by-step explanation:
The right rectangular prism will be sliced
parallel to its base along the dashed line.
Select from the drop-down menus to correctly
describe the cross section formed by the slice.
The cross section is a Choose...
with an
area of Choose... ~
Answers
Answer:
The answer in the procedure
Step-by-step explanation:
we know that
The cross section formed by the slice is a square with the same dimensions of the base of rectangular prism
The length side of the square is 6 cm
The area of the cross section is equal to
[tex]A=b^{2}[/tex]
[tex]b=6\ cm[/tex]
substitute
[tex]A=6^{2}[/tex]
[tex]A=36\ cm^{2}[/tex]
Answer:
square and 36
Step-by-step explanation:
I took the test
find five solutions of the equation y=20x. select integers for values for x starting with -2 and ending with 2
Answers
Five solutions of y = 20x with integer values for x ranging from -2 to 2 are (-2, -40), (-1, -20), (0, 0), (1, 20), and (2, 40).
To find five solutions of the equation y = 20x , we can choose integer values for x starting with -2 and ending with 2, and then calculate the corresponding values of y using the given equation.
Starting with x = -2 :
y = 20(-2) = -40
So, the first solution is (-2, -40).
Moving to x = -1:
y = 20(-1) = -20
So, the second solution is (-1, -20).
At x = 0 :
y = 20(0) = 0
So, the third solution is (0, 0).
Proceeding to x = 1 :
y = 20(1) = 20
So, the fourth solution is (1, 20).
Finally, for x = 2 :
y = 20(2) = 40
So, the fifth solution is (2, 40).
Therefore, the five solutions of the equation y = 20x with integer values for x ranging from -2 to 2 are:
(-2, -40), (-1, -20), (0, 0), (1, 20), and (2, 40).
Find the area of the circle d=8in
Answers
Answer: 64π
Step-by-step explanation: A = (d)^2 π
64 x π
64π
What is the sum of the fractions below? 3/5x+9/5x
Answers
[tex]\dfrac{3}{5x}+\dfrac{9}{5x}=\dfrac{12}{5x}[/tex]
The sum of the given expression will be equal to 12 / 5x.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
The given expression is:-
[tex]=\dfrac{3}{5x}+\dfrac{9}{5x}[/tex]
[tex]= \dfrac{3+9}{5x}[/tex]
[tex]=\dfrac{12}{5x}[/tex]
Therefore the sum of the given expression will be equal to 12 / 5x.
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Which represents the solution(s) of the graphed system of equations, y = x2 + 2x – 3 and y = x – 1?
(1, 0) and (0, –1)
(–2, –3) and (1, 0)
(0, –3) and (1, 0)
(–3, –2) and (0, 1)
Answers
Answer:
Second option: (-2,-3) and (1,0)
Step-by-step explanation:
Given the system of equations [tex]\left \{ {{y = x^2 + 2x-3} \atop {y = x - 1}} \right.[/tex], you can rewrite them in this form:
[tex]x^2 + 2x-3= x - 1[/tex]
Simplify:
[tex]x^2 + 2x-3-x+1=0\\\\x^2+x-2=0[/tex]
Factor the quadratic equation. Choose two number whose sum be 1 and whose product be -2. These are: 2 and -1, then:
[tex](x+2)(x-1)=0\\\\x_1=-2\\\\x_2=1[/tex]
Substitute each value of "x" into any of the original equation to find the values of "y":
[tex]y_1= (-2) - 1=-3\\\\y_2=(1)-1=0[/tex]
Then, the solutions are:
(-2,-3) and (1,0)
ANSWER
The solutions are (-2,-3) and (1,0).
EXPLANATION
The given system has equations:
[tex]y = {x}^{2} + 2x - 3[/tex]
and
[tex]y = x - 1[/tex]
We equate both equations:
[tex] {x}^{2} + 2x - 3 = x - 1[/tex]
[tex] {x}^{2} + 2x - x - 3 + 1 = 0[/tex]
[tex] {x}^{2} + x - 2 = 0[/tex]
[tex](x - 1)(x + 2) = 0[/tex]
This implies that,
[tex]x = - 2 \: or \: x = 1[/tex]
When x=-2 , y=-2-1=-3
When x=1, y=1-1=0
The solutions are (-2,-3) and (1,0)
need help asap please
Answers
Answer:
y = -7
Step-by-step explanation:
The easisest way to find the slope of this line is to use slope-intercept form.
Slope-intercept form:
y = mx + b
Where m = slope and b = y -intercept
In this graph, the y-intercept is -7. However, the line doesn't have a slope since its a straight horizontal line.
So, the mx part of the equation isn't a part of this new equation.
So, your equation would just y = -7