Write the equation of the line that contains the point (3, -6) and has slope -1/3 in slope-intercept form.

To write the equation of the line that contains the point (3, -6) and has a slope of \(-\frac{1}{3}\), we use the slope-intercept form of a line, which is:

\[ y = mx + b \]

where \(m\) is the slope and \(b\) is the y-intercept.

Given:
- Slope (\(m\)) = \(-\frac{1}{3}\)
- Point (\(x_1, y_1\)) = (3, -6)

First, we substitute the slope and the coordinates of the given point into the equation:

\[ y_1 = mx_1 + b \]

Substitute \(x_1 = 3\), \(y_1 = -6\), and \(m = -\frac{1}{3}\):

\[ -6 = -\frac{1}{3}(3) + b \]

Simplify the equation:

\[ -6 = -1 + b \]

Solve for \(b\):

\[ b = -6 + 1 \]
\[ b = -5 \]

Now, we have the slope (\(m\)) and the y-intercept (\(b\)), so the equation of the line in slope-intercept form is:

\[ y = -\frac{1}{3}x - 5 \]

Thus, the equation of the line is:

\[ \boxed{y = -\frac{1}{3}x - 5} \]

Do you have any questions or need further details?

Here are 8 related questions to expand your understanding:

1. How do you find the slope-intercept form of a line given two points?
2. What is the point-slope form of a line, and how is it used?
3. How do you convert from point-slope form to slope-intercept form?
4. What are the different forms of the equation of a line?
5. How do you find the equation of a line parallel to a given line?
6. How do you find the equation of a line perpendicular to a given line?
7. How do you determine if a point lies on a given line?
8. What is the standard form of a line, and how do you convert to it?

**Tip:** Always double-check your calculations for the slope and y-intercept to ensure accuracy in your final equation.

Learn how to write the equation of a line with slope -1/3 passing through point (3, -6) using the slope-intercept form. This problem involves calculating the slope, substituting values into the equation, and solving for the y-intercept. Suitable for Grades 7-9 students learning about linear equations.

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