Write an equation for the perpendicular line to the line whose equation is 4y-5x=20 that contains the point (-2,-3)
1 answer:
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 = x + 5 ← in slope-intercept form
with slope m =
given a line with slope m then the slope of a line perpendicular to it is
= -
, hence
= - 1 /
= -
y = - x + c ← is the partial equation
to find c substitute (- 2, - 3) into the partial equation
- 3 = + c ⇒ c = -
y = - x -
← in slope-intercept form
multiply all terms by 5
5y = - 4x - 23 ( add 4x to both sides )
4x + 5y = - 23 ← in standard form
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