Question

Which of the following is the equation of a line perpendicular to the line y=-10x+1, passing through the point (5,7)?

A.) 1/10 x-y = -13/2

B.) 1/10 x + y = -13/2

C.) -1/10 x - y = 13/2

D.) -1/10 x + y = -13/2

Answer 1

The equation of the line y = - 10x + 1 and the point is (5, 7).

The equation y = - 10x + 1 is already adjusted in slope-intercept form y = mx + b, where m = slope and b = y-intercept.

The slope of line y = - 10x + 1 is - 10.

We know that " If the two lines are perpendicular then their slopes are negative reciprocals to each other ".

Therefore, the slope of perpendicular line is 1/10.

To find the y-intercept of perpendicular line, substitute m = 1/10 and (x, y) = (5, 7) in the in slope-intercept form y = mx + b.

(7) = (1/10)(5) + b

7 = 1/2 + b

Subtract 1/2 from each side.

b = 7 - 1/2 = [7(2) - 1]/2 = (14 - 1)/2 = 13/2.

The perpendicular line equation is y = (1/10)x + 13/2.

Write the above equation in the form Ax + By = C.

Subtract (1/10)x from each side.

y - (1/10)x = 13/2

- (1/10)x + y = 13/2

Multiply each side by negative one.

(1/10)x - y = - 13/2

The option A is correct.