Write the equation of the line that is perpendicular to 5x+8y=16 and passes through (-5,7).

In order to do this problem, we should first put the equation in slope-intercept form, and then consider the relationship between the slopes of perpendicular lines. 
Slope Intercept form (y=mx + b), m=slope, b=y-intercept
5x + 8y = 16         Subtract 5x from both sides
8y=-5x + 16          Divide both sides by 8
y= (-5/8)x  + 2

This is our line in slope-intercept form. What will the slope be of a line that is perpendicular to this one? It will be the opposite inverse of the slope of our equation. The opposite inverse means flipping the numerator and denominator, and multiplying by negative one.
Our slope = -5/8, so the opposite inverse is 8/5.

The slope of our perpendicular line will be 8/5
In slope intercept form, our line will be 
y=(8/5)x + b
We know it passes through the point (-5,7), so we can plug in -5 for x and 7 for y in order to find b:
7 = (8/5) * -5 + b
7 = 8 *-1 + b        Add 8 to both sides
15 = b
Plugging in b, we can get our general function in slope-intercept form:

y= (8/5)x + 15