Question

If two lines are perpendicular,then the slope of one is thenegative reciprocal of the slopeof the other. What is the slopeof the line that is perpendicularto the line 5x - 2y = 7?

Answer 1

$\begin{gathered} \text{Given} \\ 5x-2y=7 \end{gathered}$

First, convert the given equation into slope-intercept form by solving in terms of y

$\begin{gathered} 5x-2y=7 \\ -2y=-5x+7 \\ \frac{-2y}{-2}=\frac{-5x+7}{-2} \\ y=\frac{5x}{2}-\frac{7}{2} \\ \\ \text{The slope of the line therefore is }m=\frac{5}{2}. \end{gathered}$

Get the negative reciprocal of the slope and we get

$\begin{gathered} \frac{5}{2}\Longrightarrow-\frac{2}{5} \\ \\ \text{Therefore, the slope of the line that is perpendicular to the line} \\ 5x-2y=7\text{ is }-\frac{2}{5} \end{gathered}$