geometry question in college algebra

Question

Find a general form of an equation of the line through the point A that satisfies the given condition.

A(7, 6); perpendicular to the line 5x + 4y = 9

Answer 1

line 5x+4y=9 is the same as

4y= -5x +9 or

y = (-5/4)x + 9/4 which has slope = -5/4

the perpendicular has slope equal to the negative inverse of -5/4 or 4/5. Just change the sign and flip the fraction upside down

y= (4/5) x + b, now plug in the point (7,6) to find b

6=(4/5)7 + b

b = 6-28/5 = 30/5 - 28/5 = 2/5

b = 2/5

y= (4/5)x + 2/5