line a is perpendicular to line b

Question

line a is perpendicular to line b. Line a passes through the points ((4,6) and (0,9). Line b passes through the point (3,-2). Find the equation of line b in slope intercept form.

Answer 1

line a is through (4,6) and (0,9) has slope (6-9)/(4-0) = -3/4 = m

the general form of the equation of the line is y=mx+b where m= slope

and b = the y intercept = 9

line a is y=-3x/4 +9

the perpendicular line b has a negative inverse slope. 4/3 Just take -4/3, change its sign and flip it upside down

y=4x/3 + b solve for b by plugging in the point (3,-2) x=3, y=-2

-2 = 4(3)/3 +b

b=-2-4 =-6

the perpendicular line b is y=4x/3 - 6 in slope intercept form