Question

Let line A be the graph of 5x + 8y = -9. Line B is perpendicular to line A and passes through the point (10,10). If line B is the graph of the equation y=mx +b, then find m+b.

Answer 1

Find slope of line A:
Move into slope-intercept form y = mx+b

5x + 8y = -9
8y = -5x - 9
y = (-5/8)x - 9/8

The slope of line A is -5/8.

If Line B is perpendicular to line A, then

slope Line B = negative reciprocal of slope Line A
slope Line B = 8/5

So like B has the equation

y = (8/5)x + b

If it passes through (10,10), we know that when x = 10, y = 10. Use those values to solve for b:

y = (8/5)x + b
10 = (8/5)·10 + b
10 = (8)·2 + b
10 = 16 + b
b = -6

So line B has equation
y = (8/5)x - 6

m = 8/5 and b = -6

so

m + b = 8/5 - 6 = 8/5 - 30/5 = -22/5

So m+b = -22/5 or -4.4 in decimal form