Answer:
The equation parallel to the line is y = -5x - 33
The equation perpendicular to the line is:
[tex]y\text{ = }\frac{1}{5}x\text{ +}\frac{17}{5}[/tex]Explanations:
The equation parallel to the line y = mx + c and passing through the point
(x₁, y₁) is given as:
[tex]y-y_1=m(x-x_1)_{}[/tex]
The equation perpendicular to the line y = mx + c and passing through the point
(x₁, y₁) is given as:
[tex]y-y_1=\frac{-1}{m}(x-x_1)[/tex]
Comapring the line y = -5x + 8 to y = mx + c:
m = -5
The line parallel to the line y = -5x+8 and passing through the point (-7, 2) will be:
[tex]\begin{gathered} y\text{ - 2 = -5(x-(-7))} \\ y\text{ - 2 = -5(x+7)} \\ y\text{ - 2 = -5x - 35} \\ y\text{ = -5x - 35 + 2} \\ y\text{ = -5x - 33} \end{gathered}[/tex]
The line perpendicular to the line above and passing through the point (-7, 2) will be:
[tex]\begin{gathered} y\text{ - 2 = }\frac{-1}{-5}(x\text{ - (-7))} \\ y\text{ - 2 = }\frac{1}{5}x\text{ + }\frac{7}{5} \\ y\text{ = }\frac{1}{5}x\text{ + }\frac{7}{5}+2 \\ y\text{ = }\frac{1}{5}x\text{ +}\frac{17}{5} \end{gathered}[/tex]
