Answer
Answer B
Work Step by Step
We can see the graph of a line passes through two points $(0,-4)$ and $(3,-2)$
Obtain: $y-y_1=\frac{y_1-y_2}{x_1-x_2}(x-x_1)\\
y-(-4)=\frac{-4-(-2)}{0-3}(x-0)\\y+4=\frac{-2}{-3}(x)\\
y+4=\frac{2}{3}x\\y=\frac{2}{3}x-4$
Find the inverse of the above equation:
$y=\frac{2}{3}x-4\\x=\frac{2}{3}y-4\\x+4=\frac{2}{3}y\\\frac{3}{2}(x+4)=(\frac{2}{3}y)\frac{3}{2}\\\frac{3}{2}(x+4)=y\\\frac{3}{2}x+6=y\\y=\frac{3}{2}x+6$
Hence, the correct answer is B.
