what is an equation of the line that passes through the points (-2, -1) and (4, 8)?

Explanation:

Step1: Calculate the slope

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1=-2,y_1 = - 1,x_2=4,y_2 = 8$. So, $m=\frac{8-(-1)}{4-(-2)}=\frac{8 + 1}{4+2}=\frac{9}{6}=\frac{3}{2}$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. We can use the point $(-2,-1)$ and $m=\frac{3}{2}$. Substituting these values, we get $y-(-1)=\frac{3}{2}(x - (-2))$, which simplifies to $y + 1=\frac{3}{2}(x + 2)$.

Step3: Convert to slope - intercept form

Expand the right - hand side: $y+1=\frac{3}{2}x+3$. Then subtract 1 from both sides to get $y=\frac{3}{2}x+2$.

Answer:

$y=\frac{3}{2}x + 2$