Write the equation of the line that perpendicular to 4x+5y=20 an that passes through the point (-4,1)

y = (5/4)x + 6

Step-by-step explanation:

The 1st line's equation is:

● 4x + 5y = 20

Substract 4x from both sides

● 4x + 5y - 4x = 20 - 4x

● 5y = 20 -4x

● 5y = -4x + 20

Divide both sides by 5

● 5y/5 = (-4x + 20)/5

● y = (-4/5)x + 4

● y = -0.8x + 4

Let m be the slope of the second line

The lines are perpendicular so the product of their slopes equals -1

Then: m × (-0.8) = -1

● m × (-0.8)= -1

● m = -1/(-0.8)

● m = 1.25

y = 1.25x + b

b is the y-intercept of the line.

To get it replace by the coordinates of a point.

We are given that the line passes through (-4,1)

● y = 1.25x + b

● 1 = 1.25 × (-4) + b

1.25 is 5/5

● 1 = (5/4) × (-4) + b

● 1 = -5 + b

Add 5 to both sides

● 1 + 5 = -5 + b + 5

● b = 6

So the equation is

● y = (5/4)x + 6