Question

Find the equation of the line that is perpendicular to y= -8x+2 and contains the point (-4,1)

Answer 1

The Solution:

Given:

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

Step 1:

Find the slope of a line that is perpendicular to the given line.

The slope is:

`m_2=(-1)/(m_1)`

Where:

`\begin{gathered} m_1=the\text{ slope of the given line}=-8 \\ m_2=the\text{ slope of a perpendicular line}=? \end{gathered}`
`m_2=(-1)/(-8)=(1)/(8)`

The formula for the equation of a line is:

`\begin{gathered} y-y_1=m_2(x-x_1) \\ \\ (x_1=-4,y_1=1) \end{gathered}`

Substitute:

`y-1=(1)/(8)(x--4)`
`\begin{gathered} y-1=(1)/(8)(x+4) \\ \\ y=(1)/(8)x+(1)/(2)+1 \\ \\ y=(1)/(8)x+(3)/(2) \end{gathered}`

Therefore, the correct answer is:

`y=(1)/(8)x+(3)/(2)`