Question

Find the equation of a line perpendicular to x−5y=4 that contains the point (−1,2). Write the equation in slope-intercept form

Answer 1

Answer:

y = - 5x - 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 )

Given

x - 5y = 4 ( subtract x from both sides )

- 5y = - x + 4 ( divide the terms by - 5 )

y = $\frac{1}{5}$ x - $\frac{4}{5}$ ← in slope- intercept form

with slope m = $\frac{1}{5}$

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

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

y = - 5x + c ← is the partial equation

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

2 = 5 + c ⇒ c = 2 - 5 = - 3

y = - 5x - 3 ← equation of perpendicular line