Question

What is the equation of the line that has a slope of 1/3 and goes through the point (6,−2)?

A. y = 1/3x − 4
B. y = 1/3x + 4
C. y = 1/3x − 8
D. y = 1/3x

Answer 1

Answer: A) y = 1/3x − 4

Explanation:

Find the Equation Using Point-Slope Formula

slope: 1/3

point: (6, −2)

Use the slope 1 and a given point (6, −2) to substitute for
`x_1` and
`y_1` in the point-slope form

y -
`y_1` = m(x -
`x_1`), which is derived from the slope equation m =
`(y_2-y_1)/(x_2-x_1)`

y − (−2) = 1/3 ⋅ (x − (6))

Simplify the equation and keep it in point-slope form.

y + 2 = 1/3 ⋅ (x − 6)

Solve for y.

1/3 ⋅ (x − 6).

Apply the distributive property.

y + 2 = 1 /3 x + 1 /3 ⋅ − 6

Combine 1/3 and x.

y + 2 = x/3 +1/3 ⋅ −6

Cancel the common factor of 3.

y + 2 = x /3 − 2

Move all terms not containing y to the right side of the equation.

Subtract 2 from both sides of the equation.

y = x/3 − 2 − 2

Subtract 2 from −2. x

y = x/3 − 4

Reorder terms.

y = 1/3x − 4

List the equation in different forms.

Slope-intercept form:

y = 1/3x − 4

Point-slope form:

y + 2 = 1/3 ⋅ (x − 6)