Question

Write an equation for the perpendicular line to the line whose equation is 4y-5x=20 that contains the point (-2,-3)

Answer 1

Answer:

4x + 5y = - 23

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 4y - 5x = 20 into this form

add 5x to both sides

4y = 5x + 20 ( divide all terms by 4 )

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

with slope m = $\frac{5}{4}$

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

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

$m_{perpendicular}$ = - 1 / $\frac{5}{4}$ = - $\frac{4}{5}$

y = - $\frac{4}{5}$ x + c ← is the partial equation

to find c substitute (- 2, - 3) into the partial equation

- 3 = $\frac{8}{5}$ + c ⇒ c = - $\frac{23}{5}$

y = - $\frac{4}{5}$ x - $\frac{23}{5}$ ← in slope-intercept form

multiply all terms by 5

5y = - 4x - 23 ( add 4x to both sides )

4x + 5y = - 23 ← in standard form