Precalculus question

Question

Write the equation of the line that passes through the point (4,2) and is perpendicular to the line passing through the point (-2,3) and (6,-3)

Answer 1

(-2,3) and (6,-3) have a line through them with equation

with slope = 6/-8=-3/4

perpendicular line has the negative inverse slope=4/3

take -3/4, change its sign and flip it upside down

perpendicular line is

y = 4x/3 +b, to solve for b=y intercept, plug in the point (4,2), x=4, y=2

2 = 4(4)/3 +b

6=16+3b

b = -10/3

y = 4x/3 -10/3 in slope intercept form

or

4x-3y =10 in standard form is the equation of the perpendicular line through the pont (4,2)