Question

The equation of line WX is 2x+y=-5. What is the equation of a line perpendicular to line WX in slope-intercept form that contains point (-1,-2)?

Answer 1

Answer:

see explanation

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 + y = - 5 into this form by subtracting 2x from both sides

y = - 2x - 5 ← in slope- intercept form

with slope m = - 2

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

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

y = $\frac{1}{2}$ x + c ← is the partial equation of the perpendicular line

To find c substitute (- 1, - 2) into the partial equation

- 2 = - $\frac{1}{2}$ + c ⇒ c = - $\frac{3}{2}$

y = $\frac{1}{2}$ x - $\frac{3}{2}$ ← equation in slope- intercept form