Answer:
Therefore, the equation of the line that passes through the point (-5,5) and has a slope of -8/5 will be:
[tex]y=\frac{-8}{5}x-3[/tex]
Step-by-step explanation:
Given the point (-5, 5)
slope = m = -8/5
Using the slope intercept form:
[tex]y=mx+b[/tex]
Plugging point (-5, 5) and slope = m = -8/5 in the slope intercept form to find the y-intercept 'b'.
[tex]5=\frac{-8}{5}\left(-5\right)+b[/tex]
[tex]\mathrm{Switch\:sides}[/tex]
[tex]\frac{-8}{5}\left(-5\right)+b=5[/tex]
[tex]8+b=5[/tex]
[tex]8+b-8=5-8[/tex]
[tex]b=-3[/tex]
so the equation of the line will be:
[tex]y=mx+b[/tex]
plugging m = -8/5 and b = -3 in slope intercept form
[tex]y=\frac{-8}{5}x-3[/tex]
Therefore, the equation of the line that passes through the point (-5,5) and has a slope of -8/5 will be:
[tex]y=\frac{-8}{5}x-3[/tex]
