Answer:
A. [tex]y=-\dfrac{8}{7}x-\dfrac{18}{7}[/tex]
Step-by-step explanation:
Let [tex]y=mx+b[/tex] be the equation of the perpendicular line.
Two perpendicular lines have slopes with product equal to -1. The slope of the given line is [tex]\frac{7}{8}[/tex] Hence,
[tex]\dfrac{7}{8}\cdot m=-1\\ \\m=-\dfrac{8}{7}[/tex]
is the slope of needed line.
This line passes through the point (-4,2), so its coordinates satisfy the equation:
[tex]2=-\dfrac{8}{7}\cdot (-4)+b\\ \\b=2-\dfrac{32}{7}=-\dfrac{18}{7}[/tex]
Therefore, the equation of the line is
[tex]y=-\dfrac{8}{7}x-\dfrac{18}{7}[/tex]
