Answer:
y = (8/5)x + 15
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