Answer:
The equation in the slope-intercept form will be:
[tex]y=-\frac{5}{4}x+1[/tex]
Step-by-step explanation:
Given
As we know that the equation of a line in point-slope form is
[tex]y-y_1=m\left(x-x_1\right)[/tex]
substituting the values m = -5/4 and point = (8, -9)
[tex]y-\left(-9\right)=\frac{-5}{4}\left(x-8\right)[/tex]
[tex]y+9=\frac{-5}{4}\left(x-8\right)[/tex]
Writing the equation in slope-intercept form
[tex]y=mx+b[/tex]
where m is the slope, and b is the y-intercept
so the equation of the line in slope-intercept form becomes
[tex]y+9=\frac{-5}{4}\left(x-8\right)[/tex]
subtract 9 from both sides
[tex]y+9-9=\frac{-5}{4}\left(x-8\right)-9[/tex]
[tex]y=-\frac{5}{4}x+1[/tex]
Therefore, the equation in the slope-intercept form will be:
[tex]y=-\frac{5}{4}x+1[/tex]
