what is an equation of the line that passes through the points (4, -2) and (-1, 3)?

Explanation:

Step1: Find the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(4,-2)$ and $(x_2,y_2)=(-1,3)$. Then $m=\frac{3 - (-2)}{-1 - 4}=\frac{3 + 2}{-5}=\frac{5}{-5}=-1$.

Step2: Use the point - slope form

The point - slope form is $y - y_1=m(x - x_1)$. Using the point $(4,-2)$ and $m = - 1$, we have $y-(-2)=-1(x - 4)$.

Step3: Simplify the equation

$y + 2=-x + 4$, which simplifies to $y=-x+2$.

Answer:

$y=-x + 2$