Question

Write the equation of the line perpendicular to 4x – 5y = -10 through the point (2, 3). explain please

Answer 1

Answer:

y =-5/4x +11/2

Step-by-step explanation:

First we need to find the slope of the line

4x-5y = 10

Solve for y

Subtract 4x from each side

4x-4x-5y =-4x-10

-5y = -4x-10

Divide by -5

-5y/-5 = -4x/-5 -10/-5

y = 4/5x +2

The slope is 4/5

The slope of a line that is perpendicular is the negative reciprocal

m perpendicular = - (5/4)

We know have a slope = -5/4 and a point (2,3)

We can use the point slope form of a line

y-y1 = m(x-x1)

y-3 = -5/4 (x-2)

Distribute

y-3 =-5/4x +10/4

Add 3 to each side

y-3+3 = -5/4 x +5/2 +3

Get a common denominator

y = -5/4x +5/2 +6/2

y =-5/4x +11/2