write an equation that represents the line. use exact numbers.

Explanation:

Step1: Find the slope

The line passes through points $(0, - 4)$ and $(1,-6)$. The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1 = 0,y_1=-4,x_2 = 1,y_2=-6$. So $m=\frac{-6-(-4)}{1 - 0}=\frac{-6 + 4}{1}=-2$.

Step2: Find the y - intercept

The y - intercept $b$ is the y - value when $x = 0$. From the point $(0,-4)$, we can see that $b=-4$.

Step3: Write the equation

The slope - intercept form of a line is $y=mx + b$. Substituting $m=-2$ and $b = - 4$ into the equation, we get $y=-2x-4$.

Answer:

$y=-2x - 4$