Step 1: Find the slope:
[tex]m= \dfrac{y_2-y_1}{x_2-x_1}= \dfrac{-2-7}{4-(-2)} = \dfrac{-9}{6}= -\dfrac{3}{2}[/tex]
This gives you [tex]y=-\dfrac{3}{2}x+b[/tex], but we need to find b.
To find b, substitute in one (x,y) pair and it doesn't matter which one. I'll go with (4,-2):
[tex]\begin{aligned}-2&=-\dfrac{3}{2}(4)+b\\[0.5em]-2&=-6+b\\[0.5em]4&=b\end{aligned}[/tex]
Now take that b-value and plug in into the slope-intercept form:
[tex]y=-\dfrac{3}{2}x+4[/tex]
It's always a good idea to toss in the other x-value from the other point, to make sure it checks out.
