Answer
$y=-6x+2.25$
Work Step by Step
Target: $y=mx+b,$ (find m and b).
Given $(x_{1},y_{1})=(0.5,-0.75)$ and $(x_{2},y_{2})=(1,-3.75)$ on a line,
calculate the slope :
$m=\displaystyle \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$
$=\displaystyle \frac{-3.75-(-0.75)}{1-0.5}$
$=\displaystyle \frac{-3}{0.5}$
$=-6$
So, the form of our linear equation is $y=-6x+b$
To find b, substitute the coordinates of one of the given points and solve for b.
$-0.75=-6(0.5)+b$
$-0.75=-3+b\qquad/+3$
$2.25=b$
Thus,
$y=-6x+2.25$
