The question asks to use the point-slope form to write the equation of a line that passes through the point (-2, -10) with a slope of $\frac{1}{3}$.

Point-Slope Form:

The point-slope form of the equation of a line is: $y - y_1 = m(x - x_1)$ where:

• $m$ is the slope of the line,
• $(x_1, y_1)$ is a point on the line.

Substituting Given Values:

Here:

• $m = \frac{1}{3}$,
• $(x_1, y_1) = (-2, -10)$.

Substitute these values into the formula: $y - (-10) = \frac{1}{3}(x - (-2))$

Simplify: $y + 10 = \frac{1}{3}(x + 2)$

Final Answer in Point-Slope Form:

$y + 10 = \frac{1}{3}(x + 2)$

Let me know if you'd like to expand this further into slope-intercept form or perform any other modifications.

Follow-up Questions:

1. How do you convert this equation into slope-intercept form?
2. What does the graph of this equation look like?
3. How do you find the y-intercept from this equation?
4. How would this equation change if the slope were negative?
5. Can you verify a point, such as $(1, -9)$, lies on this line?

Tip:

When using the point-slope form, always double-check your substitutions for $x_1, y_1,$ and $m$ to avoid errors.