Parallel/Perpendicular Through Point

Question

What is an equation of the line that passes through the point (-5,2)(−5,2) and is parallel to the line 4x-5y=54x−5y=5?

Answer 1

4x -5y = 5

5y = 4x-5

y = 4x/5 -1 is a line with slope = 4/5

y=4x/5 + b, plug in the point to find b= y intercept

2 = 4(-5)/5 + b

2 =-4 + b

b = 2+4=6

y = 4x/5 + 6 is the parallel line through (-5,2) in slope intercept form

or

4x-5y = -30 in standard form

or

4x-5y+30 = 0 in general form