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Yes, let's solve both problems and express the equations in slope-intercept form. 

The slope-intercept form of a line is:

\[
y = mx + b
\]

Where:
- \(m\) is the slope,
- \(b\) is the y-intercept.

### Problem 9:
Given:
- Point: \((3, 3)\)
- Slope: \(m = -\frac{1}{6}\)

We use the point-slope form equation:

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

Substituting the values:

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

Simplifying:

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

Add 3 to both sides:

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

Convert 3 to a fraction to combine:

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

\[
y = -\frac{1}{6}x + \frac{7}{2}
\]

So, the equation in slope-intercept form is:

\[
y = -\frac{1}{6}x + \frac{7}{2}
\]

---

### Problem 10:
Given:
- Point: \((2, -5)\)
- Slope: \(m = -\frac{5}{2}\)

Using the point-slope form:

\[
y - (-5) = -\frac{5}{2}(x - 2)
\]

Simplifying:

\[
y + 5 = -\frac{5}{2}(x - 2)
\]

Expand the right-hand side:

\[
y + 5 = -\frac{5}{2}x + 5
\]

Subtract 5 from both sides:

\[
y = -\frac{5}{2}x + 5 - 5
\]

\[
y = -\frac{5}{2}x
\]

So, the equation in slope-intercept form is:

\[
y = -\frac{5}{2}x
\]

---

Let me know if you'd like the equations in standard form as well! Do you have any questions on the process?

### Related Questions:
1. How do you convert from slope-intercept form to standard form?
2. How can you find the slope if two points are given?
3. What is the point-slope form, and when is it useful?
4. How do you graph a line using the slope-intercept form?
5. What are the conditions for parallel and perpendicular lines based on their slopes?

### Tip:
In slope-intercept form, the slope gives you the steepness of the line, and the y-intercept tells you where the line crosses the y-axis!

Write the standard form of the equation of the line with integral coefficients through the given point with the given slope. Through (3, 3), slope = -1/6 and through (2, -5), slope = -5/2.

Learn how to find the equation of a line given a point and slope using both slope-intercept and point-slope forms. Solve problems through points (3, 3) with slope -1/6 and (2, -5) with slope -5/2. Suitable for students in Grades 8-10.

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