Answer:
[tex]y = -5x - 23[/tex]
Step-by-step explanation:
To write an equation in the slope-intercept form for a line, given the coordinates of a point on the line as well as the line's slope, we use the following formula:
[tex]\boxed{y - y_1 = m(x - x_1)}[/tex],
where [tex]m[/tex] is the slope of the line and [tex](x_1, y_1)[/tex] are the given coordinates of a point.
In this question, we are told that the slope is -5 and the coordinates of a point passing through the point are (-3, -8).
Therefore, using the above formula, we can write:
[tex]y - (-8) = -5(x - (-3))[/tex]
⇒ [tex]y + 8 = -5(x + 3)[/tex]
⇒ [tex]y + 8 = -5x - 15[/tex] [Distributing -5 into the brackets]
⇒ [tex]y = -5x - 15 - 8[/tex] [Subtracting 8 from both sides]
⇒ [tex]y = -5x - 23[/tex]
This means that the equation for the slope-intercept form of the line is [tex]y = -5x - 23[/tex] .
Learn more about the slope-intercept form here:
https://brainly.com/question/27803801
