Question

Find the equation of the line thatis perpendicular to y = 4x + 5 andcontains the point (8, -4).

Answer 1

The Solution:

Given:

`y=4x+5`

Required:

Find the equation of the line that passes the point (8,-4) and it is perpendicular to y = 4x + 5.

Step 1:

Find the slope of y = 4x+5.

Comparing the line y = 4x +5 and y = mx + c.

The slope of the line is:

`slope=m=4`

Thus, for a line that is perpendicular to y = 4x + 5, the slope is:

`slope=m_2=(-1)/(m)=(-1)/(4)`

Step 2:

Find the required equation of the perpendicular line.

`\begin{gathered} y-y_1=m_2(x-x_1) \\ \\ x_1=8 \\ y_1=-4 \end{gathered}`

Substitute:

`\begin{gathered} y--4=(-1)/(4)(x-8) \\ \\ y+4=(-1)/(4)(x-8) \\ \\ y=-(1)/(4)x+2-4 \\ \\ y=-(1)/(4)x-2 \end{gathered}`

Answer:

`y=-(1)/(4)x-2`