To find the slope of a line from its equation, you have to put the equation in the form
[tex]y=mx+b[/tex]
Where m is the slope
Since the given equation is
[tex]2x-7y=-5[/tex]
Add 7y to both sides
[tex]\begin{gathered} 2x-7y+7y=-5+7y \\ 2x=-5+7y \end{gathered}[/tex]
Add 5 to both sides
[tex]\begin{gathered} 2x+5=-5+5+7y \\ 2x+5=7y \end{gathered}[/tex]
Switch the 2 sides
[tex]7y=2x+5[/tex]
Divide all terms on both sides by 7
[tex]\begin{gathered} \frac{7y}{7}=\frac{2x}{7}+\frac{5}{7} \\ \\ y=\frac{2}{7}x+\frac{5}{7} \end{gathered}[/tex]
The slope of the given line is
[tex]m=\frac{2}{7}[/tex]
Since parallel lines have the same slopes, then
The slope of the parallel line is 2/7
Since the product of the slopes of the perpendicular lines is -1, then
To find the slope of the perpendicular line reciprocal of the value and change the sine
Then the slope of the perpendicular line is
[tex]m_P=-\frac{7}{2}[/tex]
The slope of the perpendicular line is -7/2
