Equation question

Question

Write the equation of a line that passes through point (-8, 0) and is perpendicular to line 3x - 5y = 6

Answer 1

(1) Use general equation of a straight line y = mx + b, where m is gradient, b is y intercept

(2) Use property of perpendicular lines that m1.m2 = -1

For 3x - 5y = 6 rearrange to match above general equation

=> 5y = 3x - 6

=> y = 3/5 x - 6/5

hence gradient is 3/5

substitute this in gradients equation to give 3/5 x m2 = -1

=> m2 = -1 x 5/3 = -5/3

so equation of perpendicular line is y = b - 5/3 x

don't know b yet, but we know it passes through (-8,0) so substitute these values:

0 = b - 5/3 (-8)

=> 0 = b + 40/3

=> b = -40/3 [OR -13 1/3]

final equation is therefore y = -40/3 - 5/3 x OR 3y = -40 - 5x OR -3y = 40 + 5x