Question

Which lines are perpendicular to the line y - 1 = 1/3(x+2)? Check all that apply.

A. y + 2 = -3(x-4)

B. y - 5 = 3(x+11)

C. y = -3x - 5/3

D. y = 1/3x - 2

E. 3x + y = 7

Answer 1

To find lines perpendicular to a given line, we need to find the slope of the given line and then look for lines with slopes that are negative reciprocals. The lines that are perpendicular to the given line are A, C, and E.

Step-by-step explanation:

To determine which lines are perpendicular to the given line, we need to find the slope of the given line and then look for lines with slopes that are negative reciprocals of the given slope.

The given line is y - 1 = ⅓(x+2).

We can rewrite this equation in slope-intercept form as y = ⅓x + ⅓.

The slope of the given line is ⅓.

To be perpendicular, the slopes of the other lines must be negative reciprocals of ⅓ which is -3.

The lines that are perpendicular to the given line are:

A. y + 2 = -3(x-4)

C. y = -3x - 5/3

E. 3x + y = 7

Answer 2

The slope of the given line is 1/3.

The perpendiculars all have the negative reciprocal slope, -3.

A. y + 2 = -3(x-4)

Yes, slope -3.

B. y - 5 = 3(x+11)

No, slope 3.

C. y = -3x - 5/3

Yes, slope -3.

D. y = 1/3 x - 2

No, that's slope 1/3.

E. 3x + y = 7

That's

y = -3x + 7

Another slope -3, Yes.