Question

Write the equation of a line that is perpendicular to the given line and that passes through the given point. y= 2/3x + 9 ; (–6, 5)

Answer 1

Answer:

y = - $\frac{3}{2}$ x - 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = $\frac{2}{3}$ x + 9 ← is in slope- intercept form

with slope m = $\frac{2}{3}$

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{\frac{2}{3} }$ = - $\frac{3}{2}$, thus

y = - $\frac{3}{2}$ x + c ← is the partial equation

To find c substitute (- 6, 5) into the partial equation

5 = 9 + c ⇒ c = 5 - 9 = - 4

y = - $\frac{3}{2}$ x - 4 ← equation of perpendicular line