Answer
$y=\dfrac{11}{5}x+3$
Work Step by Step
Using $y-y_1=\dfrac{y_1-y_2}{x_1-x_2}(x-x_1)$ or the Two-Point Form, then the equation of the line passing through the given points, $(
-1,-2.5
)\text{ and }(
4,8.5
)$, is
\begin{array}{l}
y-(-2.5)=\dfrac{-2.5-8.5}{-1-4}(x-(-1))
\\\\
y+2.5=\dfrac{-11}{-5}(x+1)
\\\\
y+2.5=\dfrac{11}{5}(x+1)
\\\\
y+2.5=\dfrac{11}{5}x+\dfrac{11}{5}
\\\\
y=\dfrac{11}{5}x+5.5-2.5
\\\\
y=\dfrac{11}{5}x+3
.\end{array}
