Hello!
First, let's discover the slope using the formula below:
[tex]\text{slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]Let's use (x1, y1) as (-1, 5) and (x2, y2) as (3, -1). Replacing it in the formula:
[tex]\text{slope}=\frac{-1_{}-(5)_{}}{3_{}-(-1)_{}}=\frac{-1-5}{3+1}=\frac{-6}{4}=-\frac{3}{2}[/tex]So, we know one part of the equation, that m = -3/2.
Now, we have to calculate b:
To do it, let's use the point (x2, y2) = (3, -1) again:
[tex]\begin{gathered} y=mx+b \\ -1=3\cdot(-\frac{3}{2})+b \\ -1=-\frac{9}{2}+b \\ -b=-\frac{9}{2}+1 \\ -b=-\frac{7}{2} \\ b=\frac{7}{2} \end{gathered}[/tex]So, we also know that b = 7/2.
