Which equation represents a line that is perpendicular to the line with equation y = 2x − 8?

Answer 1

Hi Vanessa,

For any line defined by y = mx + b , m is the slope, and b is the y-intercept.

To solve for a line parallel to y we need a line with the same slope.

y_parallel = mx + c

To solve for a line perpendicular to y we need a line whose slope is equal to the negative reciprocal of slope m.

y_{perpendicular} = -1/m*x + d.

In your case, m = 2 so we need a line with slope -1/2.

For example: y_{perpendicular} = -1/2*x +5

If your options are

A. y = 12x + 1

B. y = −12x + 1

C. x + 2y = 5

D. −x + 2y = −3

E. −x − 2y = 9

We need to solve for these in terms of y = mx + b

A. y = 12x + 1

B. y = −12x + 1

C. x + 2y = 5 → y = -1/2*x + 5

D. −x + 2y = −3 → y = 1/2*x -3/2

E. −x − 2y = 9 → y = -1/2x -9/2

Only C and E have slopes of -1/2.

Hope that helps,

Bryce

Answer 2

There are many equations that would represent that line. Do you have a point it needs to travel through. Otherwise, as long as you use a slope that is perpendicular any y-intercept satisfies your situation.

To find a perpendicular slope you need the slope 2 and find its opposite reciprocal which is -1/2.

An equation to a line perpendicular just needs that slope. All equations with that slope are perpendicular to your given line.

For example, y=-1/2x - 8 (same y-intercept, but perpendicular slope).