Answer:
[tex]y=-\frac{3}{4}x[/tex]
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 [tex]y/x=k[/tex] or [tex]y=kx[/tex]
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
[tex]A(0,0),B(4,-3)[/tex]
Find the slope m
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute
[tex]m=\frac{-3-0}{4-0}[/tex]
[tex]m=-\frac{3}{4}[/tex]
The equation of the line is equal to
[tex]y=-\frac{3}{4}x[/tex]
