Through: (-5, 5), perp. to y = 5/9x - 4

Step-by-step explanation:

The complete question is:

Find the equation of the line that passes through: (-5, 5), and is perpendicular to the line y = 5/9x - 4

step 1

Find the slope of the line

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

The equation of the given line is

The slope of the given line is

The opposite reciprocal is equal to

----> slope of the perpendicular line

step 2

Find the equation of the line in point slope form

we have

substitute

step 3

Convert to slope intercept form

Isolate the variable y