what is an equation of the line that passes through the points (-1, -2) and (-2, -5)?

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 $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $(x_1,y_1)=(-1,-2)$ and $(x_2,y_2)=(-2,-5)$. So $m=\frac{-5-(-2)}{-2 - (-1)}=\frac{-5 + 2}{-2+1}=\frac{-3}{-1}=3$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(-1,-2)$ and $m = 3$, we have $y-(-2)=3(x - (-1))$.

Step3: Simplify the equation

$y + 2=3(x + 1)$ expands to $y+2=3x+3$, and then simplifies to $y=3x + 1$.

Answer:

$y = 3x+1$