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 = [tex]\frac{5}{4}[/tex] x + 5 ← in slope-intercept form
with slope m = [tex]\frac{5}{4}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex], hence
[tex]m_{perpendicular}[/tex] = - 1 / [tex]\frac{5}{4}[/tex] = - [tex]\frac{4}{5}[/tex]
y = - [tex]\frac{4}{5}[/tex] x + c ← is the partial equation
to find c substitute (- 2, - 3) into the partial equation
- 3 = [tex]\frac{8}{5}[/tex] + c ⇒ c = - [tex]\frac{23}{5}[/tex]
y = - [tex]\frac{4}{5}[/tex] x - [tex]\frac{23}{5}[/tex] ← in slope-intercept form
multiply all terms by 5
5y = - 4x - 23 ( add 4x to both sides )
4x + 5y = - 23 ← in standard form
