Question

Find the slope of a line that is a) parallel and b) perpendicular to the given line.x + 8y = 1

Answer 1

Recall that the slope-intercept form of a line is in the form

`\begin{gathered} y=mx+b \\ \text{where} \\ m\text{ is the slope} \\ b\text{ is the y-intercept} \end{gathered}`

Given the equation x + 8y = 1, convert the equation to slope intercept form

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

Now that it is in the slope intercept form, we have determined that the slope is m = -1/8.

a.) Slope of the line that is parallel

The slope of a line parallel to the given line equation is the same slope to the line, in which case it is m = -1/8.

b.) Slope that is perpendicular to the given line

The slope of a line perpendicular to the given line is the negative reciprocal of the slope.

Solve for the negative reciprocal

`\begin{gathered} m_{\text{parallel}}=-(1)/(8) \\ m_{\text{perpendicular}}=-\frac{1}{m_{\text{parallel}}} \\ \\ m_{\text{perpendicular}}=-(1)/(-(1)/(8)) \\ m_{\text{perpendicular}}=1\cdot(8)/(1) \\ m_{\text{perpendicular}}=8 \end{gathered}`

Therefore, the slope perpendicular to the given line is m = 8.