The equation of line a is y=12x−1, and it passes through point (6,2). Line b is perpendicular to line a, and it passes through point (−6,2).

Question

Use the equation and given point to answer the questions below.

The equation of line a is y=12x−1, and it passes through point (6,2).

Line b is perpendicular to line a, and it passes through point (−6,2).

A: What is the slope of line b?

B: What is the y-intercept of line b?

Select two answers: one for A and one for B.

B: 14

B: 1

A: 1/2

A: −2

A: −1/2

B: 5

A: 2

B: -1

Answer 1

The equation of line a is y=(1/2)x−1, and it passes through point (6,2).

Line b is perpendicular to line a, and it passes through point (−6,2).

A: What is the slope of line b?

Perpendicular lines have slopes that are the negative reciprocal of each other. Since line a has a slope of (1/2), line b has a slope of -2. [note: this is: - (1/(1/2))

B: What is the y-intercept of line b?

line b is: y = -2x + c and we use point (-6,2) to find b.

2 = -2(-6) + c

14 = c

The equation for line b is: y = -2x + 14

The y-intercept (which is the point where x=0) is the point (0,14.) So, y=14

Answer 2

if line a is y = (1/2)x -1 then line b perpendicular to a has to have slope -1/(1/2) = -2

Using the point-slope form of a line: y - y₀ = m(x - x₀) and using (x₀,y₀) = (6,2) and m = -2:

y - 2 = (-2)(x - 6)

Solve for y so we will have slope-intercept form (y = mx + b, where m=slope, b=y-intercept):

y = -2x + 14

The y-intercept of line b is 14.

Answer 3

slope of a is 12. slope of b is the negative inverse -1/12, which is not among your answers.

a can't pass through the point (6,2) you have a contradiction in the problem. Plug that point into the equation for a and it doesn't fit.