Perpendicular lines

Question

Which of the following is the equation of a line perpendicular to the line y=-3/2 x + 4 passing through the point (3,9)

A.) 2x - 3y = 21

B.) -2x + 3y = 21

C.) 2x + 3y = 21

D.) -2x - 3y = 21

Answer 1

The equation is y = (-3/2)x+4

Compare the equation with slope - intercept form y = mx + b.

slope = -3/2.

Because the slopes of perpendicular lines are negative reciprocals, the slope of perpendicular line is -1/(-3/2) = 2/3.

Now, the perpendecular line equation is y = (2/3)x + b.

Find the y - intercept by substituting the point in the line equation say (x, y) = (3, 9).

9 = (2/3)(3) + b

9 = 2 + b

b = 9 - 2

⇒ b = 7

The perpendecular line equation is

y = (2/3)x +7

Multiply each side by 3

3y=3((2/3)x +7)

3y = 2x+21

-2x+3y =21

So option B is correct