what is an equation of the line that passes through the points (0, -6) and (-5, -2)?

Explanation:

Step1: Find the slope

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(0, - 6)$ and $(x_2,y_2)=(-5,-2)$. Then $m=\frac{-2-(-6)}{-5 - 0}=\frac{-2 + 6}{-5}=\frac{4}{-5}=-\frac{4}{5}$.

Step2: Use the slope - intercept form

The slope - intercept form of a line is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. We know that the line passes through the point $(0,-6)$, so when $x = 0$, $y=-6$. Substituting $x = 0$, $y=-6$ and $m=-\frac{4}{5}$ into $y=mx + b$, we get $-6=-\frac{4}{5}(0)+b$, so $b=-6$.

Step3: Write the equation of the line

Substitute $m = -\frac{4}{5}$ and $b=-6$ into $y=mx + b$. The equation of the line is $y=-\frac{4}{5}x-6$.

Answer:

$y = -\frac{4}{5}x-6$