Answer:
The equation of the line in slope-intercept form is:
Step-by-step explanation:
Given the points
Finding the slope
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-8,\:5\right),\:\left(x_2,\:y_2\right)=\left(-1,\:-5\right)[/tex]
[tex]m=\frac{-5-5}{-1-\left(-8\right)}[/tex]
[tex]m=-\frac{10}{7}[/tex]
We know the slope-intercept form of the line equation is
[tex]y = mx+b[/tex]
where m is the slope and b is the y-intercept
substituting m = -10/7 and (-8, 5) in the slope-intercept form to determine the y-intercept
[tex]5\:=\:\frac{-10}{7}\left(-8\right)+b[/tex]
[tex]\frac{80}{7}+b=5[/tex]
[tex]b=-\frac{45}{7}[/tex]
now substituting m = -10/7 and b = -45/7 in the slope-intercept form
[tex]y = mx+b[/tex]
[tex]y\:=\:\frac{-10}{7}x+\left(-\frac{45}{7}\right)[/tex]
[tex]y\:=\:\frac{-10}{7}x-\frac{45}{7}[/tex]
Thus, the equation of the line in slope-intercept form is:
