Question

Which of the following is a point-slope equation of a line with the point (-6,2)

and a slope of 1/2?
A. y-6 = 1/2(x+2)
B. y+6= 1/2 (x-2)
C. y-2 = 1/2(x+6)
D. y+2=1/2(x-6)

Answer 1

The point-slope equation of a line with the point (-6,2)

and a slope of 1/2 will be:

• y - 2 = 1/2 (x+6)

Hence, option C is true.

Explanation:

Given

• The point (-6, 2)

• The slope m = 1/2

The point-slope form:

`y-y_1=m\left(x-x_1\right)`

The point-slope form of the line equation is defined as

where

• m is the slope of the line

• (x₁, y₁) is the point

In our case:

• m = 1/2

• (x₁, y₁) = (-6, 2)

substituting m = 1/2 and (x₁, y₁) = (-6, 2) in the point-slope form of the line equation

`y-y_1=m\left(x-x_1\right)`

y - 2 = 1/2 (x - (-6))

y - 2 = 1/2 (x+6)

Therefore, the point-slope equation of a line with the point (-6,2)

and a slope of 1/2 will be:

• y - 2 = 1/2 (x+6)

Hence, option C is true.