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 \\ (-2y)/(-2)=(-5x+7)/(-2) \\ y=(5x)/(2)-(7)/(2) \\ \\ \text{The slope of the line therefore is }m=(5)/(2). \end{gathered}`

Get the negative reciprocal of the slope and we get

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