Chapter E, Problem 13.5EX

To determine

To find the equation of line perpendicular to the given line $y=\frac{2}{3}x+5$ .

Answer to Problem 13.5EX

Option (d)

Explanation of Solution

Given information: The equation of line $y=\frac{2}{3}x+5$ passing through $(-4,7)$ .

Concept used:

Two lines are perpendicular to each other, when $m_1\cdot m_2=-1$

The equation of line passing through $\left(x_1,y_1\right)$ and having slope $m$ is

  $y-y_1=m(x-x_1)$

The equation of given line is $y=\frac{2}{3}x+5$

The slope of the line perpendicular to the given line is $-\frac{3}{2}$

The equation of the line passing through $\left(-4,7\right)$ and having slope $-\frac{3}{2}$ is

  $\begin{array}{l}y-7=-\frac{3}{2}(x+4)\\ y=-\frac{3}{2}x+1\end{array}$

Hence, the equation of line is $y=-\frac{3}{2}x+1$