Question

Which of the following is the equation a line perpendicular to the line

y=-1/3x + 1 passing through the point (2,7)?

A.) 3x-y=1

B.) 3x-y=1

C.) -3x-y= 1

D.) -3x+y= -1

Answer 1

Slope - intercept form line equation is y = mx + b, where m is slope and b is y - intercept.

The line equation is y = (-1/3)x + 1 and the point is (2, 7).

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

slope = -1/3.

Because the slopes of perpendicular lines are negative reciprocals, the slope of perpendicular line is 3.

Now, the perpendecular line equation is y =  3x + b.

Find the y - intercept by substituting the point in the line equation say (x, y) = (2, 7).

7 = (3)(2) + b

b = 7 - 6

⇒ b = 1.

y = 3x + 1.

The perpendecular line equation is 3x - y = -1