Question

What is the equation in slope-intercept form of the line that passes through the point (2,-2) and is perpendicular to the line represented by y = 2/5 x + 2

Answer 1

Answer:

y = - $\frac{5}{2}$ x + 3

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 = $\frac{2}{5}$ x + 2 ← is in slope- intercept form

with slope m = $\frac{2}{5}$

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

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{\frac{2}{5} }$ = - $\frac{5}{2}$, thus

y = - $\frac{5}{2}$ x + c ← is the partial equation

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

- 2 = - 5 + c ⇒ c = - 2 + 5 = 3

y = - $\frac{5}{2}$ x + 3 ← equation of line