Answer:
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
