Answer:
[tex]\displaystyle y=-\frac{2}{3}x+\frac{5}{3}[/tex]
Step-by-step explanation:
We want to find the equation of the line that passes through the two points:
(4, -1) and (-2, 3).
First, we will find the slope of the two points. So:
[tex]\displaystyle m=\frac{3-(-1)}{-2-4}=\frac{4}{-6}=-\frac{2}{3}[/tex]
Now, we will use the point-slope form given by:
[tex]y-y_1=m(x-x_1)[/tex]
Use either point. I'm going to use (4, -1). So, substitute:
[tex]\displaystyle y-(-1)=-\frac{2}{3}(x-(4))[/tex]
Simplify and distribute:
[tex]\displaystyle y+1=-\frac{2}{3}x+\frac{8}{3}[/tex]
Subtract 1 from both sides. Therefore:
[tex]\displaystyle y=-\frac{2}{3}x+\frac{5}{3}[/tex]
