Find the equation of the following lines

Question

1. Find the equation of the following lines

a) perpendicular to the line y = 3/4 x - 2 with the same y-intercept as 5x-2y=-12
b) parallel to the line 3x + 5y - 14 = 0 passing through T (10 , -1)

Answer 1

y=3x/4 -2 has a perpendicular line with negative inverse slope = -4/3

y =-4x/3 +6

3x+5y-14=0 has a parallel line with the same slope = -3/5

y = -3x/5 + b

-1 =-30/5+ b

b = -1+6 = 5

y= -3x/5 +5 is the parallel line through (10,-1)