Question

Write the equation of a line that contains (2,-4) and that is perpendicular to y=2/3x+2

Answer 1

Answer:

y = - $\frac{3}{2}$ x - 1

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 + 2 ← 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 (2, - 4) into the partial equation

- 4 = - 3 + c ⇒ c = - 4 + 3 = - 1

y = - $\frac{3}{2}$ x - 1 ← equation of perpendicular line