Question

Please help me find the equations for the parallel and the perpendicular lines.

Answer 1

Answer:

The equation parallel to the line is y = -5x - 33

The equation perpendicular to the line is:

`y\text{ = }(1)/(5)x\text{ +}(17)/(5)`Explanations:

The equation parallel to the line y = mx + c and passing through the point

(x₁, y₁) is given as:

`y-y_1=m(x-x_1)_{}`

The equation perpendicular to the line y = mx + c and passing through the point

(x₁, y₁) is given as:

`y-y_1=(-1)/(m)(x-x_1)`

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:

`\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}`

The line perpendicular to the line above and passing through the point (-7, 2) will be:

`\begin{gathered} y\text{ - 2 = }(-1)/(-5)(x\text{ - (-7))} \\ y\text{ - 2 = }(1)/(5)x\text{ + }(7)/(5) \\ y\text{ = }(1)/(5)x\text{ + }(7)/(5)+2 \\ y\text{ = }(1)/(5)x\text{ +}(17)/(5) \end{gathered}`