Write the equation of a line perpendicular to 5x−9y=−8 that passes through the point (−5,8).

 y = -(9/5)x - 1

Step-by-step explanation:

Rewrite the equation in standard form:  y = (5/9)x+(8/9).  [y=mx+b]

A line perpendicular to this would have a slope that is the negative inverse of the original slope (5/9), which would make it -(9/5).  The y-intercept would also change, but we don't know the value, yet.  For now, we'll use "b" for the y-intercept.  This results in a perpendicular line:

y = -(9/5)x + b

We can calculate b, the y-intercept, by using the point (-5,8) and solving for b.

8 = -(9/5)*(-5) + b

8 = (9) + b

b = -1

The line perpendicular to 5x−9y=−8 that passes through the point (−5,8) is

y = -(9/5)x - 1

step-by-step explanation:

we are given

since, we have to isolate x on anyone side

so, we can move all x terms on one side

subtract both sides by 2x

add both sides by 9

divide both sides by 4

we get