Question

Which is the equation in slope-intercept form for the line that passes through (-2, 15) and is perpendicular to 2x + 3y = 4?

Answer 1

Answer:

B

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 )

Rearrange 2x + 3y = 4 into this form

Subtract 2x from both sides

3y = - 2x + 4 ( divide all terms by 3 )

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

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

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

To find c substitute (- 2, 15) into the partial equation

15 = - 3 + c ⇒ c = 15 + 3 = 18

y = $\frac{3}{2}$ x + 18 → B

Answer 2

Answer:

B and C are both perpindicular to 2x + 3y = 4.

But B passes (-2, 15).

Hope this helps!!!