What is an equation of the line that passes through point (-4,-6) and is perpendicular to the line 4x+5y=25

PLEASE ANSWER I NEED FOR GEOMETRY

y = 5x/4 - 1

Step-by-step explanation:

We are asked to find the equation of a line which is perpendicular to 4x + 5y = 25

Step 1: find the slope

4x + 5y = 25

5y = 25 - 4x

5y = -4x + 25

Divide both sides by 5 , to get the value of y

5y/5 =( -4x + 25)/5

y = ( -4x + 25)/5

Following the equation of a line

y = mx + c

Can we separate it

y = -4x/5 + 25/5

y = -4x/5 + 5

Slope m = -4/5

Step 2:

Note: if two lines are perpendicular to the other, both are negative reciprocal of each other

The slope of the line is 5/4

Using the formula of point slope form

y - y_1 = m( x - x_1)

We are provided with a point

( -4 , -6)

x_1 = -4

y_1 = -6

Insert the values

y - (-6) = m ( x - (-4))

y + 6 = m( x + 4)

m = 5/4

y + 6 = 5/4 ( x + 4)

Make y the subject of the formula

y = 5/4(x + 4) - 6

LCM = 4

y =( 5(x + 4) - 24) / 4

Open the bracket

y =( 5x + 20 - 24)/4

y = (5x - 4)/4

Following the equation of the line

y = mx + c

y = 5x / 4 - 4/4

y = 5x/ 4 - 1

Therefore, the equation of the line is

y = 5x/4 - 1