What is the equation of the line that passes through the point left parenthesis, minus, 6, comma, minus, 4, right parenthesis(−6,−4) and has a slope of 1/3

To find the equation of a line that passes through the point \((-6, -4)\) and has a slope of \(\frac{1}{3}\), we can use the point-slope form of the equation of a line:

\[
y - y_1 = m(x - x_1)
\]

Where:
- \(m\) is the slope of the line.
- \((x_1, y_1)\) is a point on the line.

Substituting the given values:
- \(m = \frac{1}{3}\)
- \((x_1, y_1) = (-6, -4)\)

The equation becomes:

\[
y - (-4) = \frac{1}{3}(x - (-6))
\]

Simplifying this:

\[
y + 4 = \frac{1}{3}(x + 6)
\]

Next, distribute the \(\frac{1}{3}\) on the right-hand side:

\[
y + 4 = \frac{1}{3}x + 2
\]

Finally, subtract 4 from both sides to put the equation in slope-intercept form (\(y = mx + b\)):

\[
y = \frac{1}{3}x + 2 - 4
\]

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

So, the equation of the line is:

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

Would you like any details on this solution or have any questions?

Here are five related questions:
1. How do you find the y-intercept of the line given the slope and a point?
2. What is the point-slope form of a line and when is it used?
3. How do you convert a line equation from point-slope form to slope-intercept form?
4. How do you find the equation of a line given two points?
5. What are parallel lines, and how do their slopes relate?

**Tip:** When dealing with linear equations, always make sure to simplify and rearrange your final answer into the desired form, such as slope-intercept or standard form.

Learn how to find the equation of a line passing through the point (-6, -4) with a slope of 1/3. This problem covers key concepts such as linear equations, slope determination, and converting equations to slope-intercept form. Suitable for Grades 7-9.

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