Question

Write the equation in slope-intercept form of a line that has a slope of One-third and passes through the point (-6, 0).
y = one-third x
y = one-third x minus 6
y = one-third x minus 2
y = one-third x + 2

Answer 1

To write the equation in slope-intercept form (y = mx + b), we start with the slope (m) and a point (x₁, y₁) that the line passes through.

Given:
- Slope (m) = \(\frac{1}{3}\)
- Point (-6, 0) (x₁ = -6, y₁ = 0)

We can use the point-slope form of the equation of a line, which is:

\[
y - y₁ = m(x - x₁)
\]

Substituting the values:

\[
y - 0 = \frac{1}{3}(x - (-6))
\]

This simplifies to:

\[
y = \frac{1}{3}(x + 6)
\]

Distributing \(\frac{1}{3}\):

\[
y = \frac{1}{3}x + \frac{6}{3}
\]

\[
y = \frac{1}{3}x + 2
\]

Thus, the equation of the line in slope-intercept form is:

\[
y = \frac{1}{3}x + 2
\]

The correct choice from your options is:

**y = one-third x + 2.**