Question

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

Explanation:

Step1: Calculate the slope

The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2-y_1}{x_2-x_1}$.
Substitute $(x_1,y_1)=(4,-2)$ and $(x_2,y_2)=(-1,3)$:
$m=\frac{3-(-2)}{-1-4}=\frac{5}{-5}=-1$

Step2: Use point-slope form

Point-slope form is $y-y_1=m(x-x_1)$. Use $(x_1,y_1)=(4,-2)$ and $m=-1$:
$y-(-2)=-1(x-4)$

Step3: Simplify to slope-intercept form

Simplify the equation:
$y+2=-x+4$
$y=-x+2$

Answer:

$y=-x+2$ (or equivalent forms like $x+y=2$)