What is an equation of a line perpendicular to 5x+8y=16 and passed through (-5,7)

y = (8/5)x + 15

Step-by-step explanation:

First change the equation to standard form (y=mx+b)

5x + 8y = 16

8y = 16 - 5x

y = - (5/8)x + (16/8)

y = - (5/8)x + 2

Perpendicular Lines have the inverse opposite sign of slope

[For example: inverse opposite sign of 2 is - (1/2)]

Original equation slope (m) : - (5/8)

2nd Equation (m) : 8/5

After finding the slope, plug in the slope and points the standard form equation (y=mx+b)

Point: (-5,7)     x : -5     y : 7

Slope (m) : 8/5

y = m x + b

7 = (8/5) (-5) + b

'b' is the y-intercept and the last thing to solve for the equation

7 = - 8 + b

15 = b

Now, put the slope (m) and y-intercept (b) back into the equation

y = (8/5)x + 15

n

step-by-step explanation: