Step-by-step explanation:
First, let's find the slope of the line. Note that it passes through P1(-8, -1) and P2(0, -5). So the slope of this line is
[tex]m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{-5 - (-1)}{0 - (-8)}[/tex]
[tex]\:\:\:\:\:= \dfrac{-4}{8} = -\dfrac{1}{2}[/tex]
The slope-intercept form of the equation can be written as
[tex]y = mx + b = -\frac{1}{2}x + b[/tex]
To solve for b, we can use either P1 or P2. Let's use P2.
[tex]-5 = -\frac{1}{2}(0) + b \Rightarrow b = -5[/tex]
Therefore, the slope-intercept form of the equation for the line is given by
[tex]y = -\frac{1}{2}x - 5[/tex]
