What is the equation of the line that passes through the point left parenthesis, minus, 6, comma, 6, right parenthesis(−6,6) and has a slope of one third 
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The equation of a line in point-slope form is given by:

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

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

In this case, the point is \( (-6, 6) \) and the slope \( m = \frac{1}{3} \). Substituting these values into the point-slope form:

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

Now, simplify the equation:

\[
y - 6 = \frac{1}{3}x + 2
\]

Add 6 to both sides to get the equation in slope-intercept form:

\[
y = \frac{1}{3}x + 8
\]

So, the equation of the line is:

\[
y = \frac{1}{3}x + 8
\]

Would you like more details or have any other questions?

### Related Questions:
1. How do you find the equation of a line given two points?
2. What is the slope of a line perpendicular to this one?
3. How would you find the x-intercept of this line?
4. Can you rewrite the equation of the line in standard form?
5. How does changing the slope affect the line's steepness?

**Tip:** Always check if the point satisfies the final equation after solving!

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

Discover how to find the equation of a line passing through the point (-6, 6) with a slope of 1/3. This solution uses key algebraic concepts such as point-slope and slope-intercept forms, making it perfect for students in Grades 8-10.

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