Question

What equation represents the linear function shown in the graph? Enter your answer in the box. Write your answer in the form y = mx + b.

Answer 1

Answer:

$y=-\frac{3}{4}x$

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form $y/x=k$ or $y=kx$

In a direct variation the constant of proportionality k  is equal to the slope m and the line passes through the origin

In this problem the line passes through the origin

therefore

The linear equation of the figure represent a direct variation

Let

$A(0,0),B(4,-3)$

Find the slope m

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute

$m=\frac{-3-0}{4-0}$

$m=-\frac{3}{4}$

The equation of the line is equal to

$y=-\frac{3}{4}x$

Answer 2

You can take the first point as the origin O(0,0) and the second one (-2,0.5) for easier calculations.
Find the slope, m = (y2 - y1)/(x2 - x1)
= -2-0 / -0.5-0 = 2/0.5 = 4

now take (x,y) = (0,0) and m= 4
use the point slope form
(y - y1) = m(x - x1)
(y - 0) = (4)(x - 0) ......taking (x1,y1) = (0,0)
y = 4x + 0 ...... in the form of y = mx + b
I hope I was helpful:)