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Let's solve this problem step by step!

You are asked to write the equation of the line using **point-slope form** and convert it into **slope-intercept form**.

### Information from the image:
- The slope of the line is \( m = -\frac{1}{7} \).
- A point on the line is \( (-2, 1) \).

### Step 1: Write the equation in 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, and \( (x_1, y_1) \) is a point on the line.

Using the point \( (-2, 1) \) and the slope \( m = -\frac{1}{7} \), we substitute these values into the formula:

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

### Step 2: Simplify and convert to slope-intercept form
Now, distribute the slope on the right-hand side:

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

Next, add 1 to both sides to isolate \( y \):

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

Since 1 is the same as \( \frac{7}{7} \), the equation becomes:

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

Simplify the constants on the right-hand side:

\[
y = -\frac{1}{7}x + \frac{5}{7}
\]

### Final Answer (Slope-Intercept Form):

\[
y = -\frac{1}{7}x + \frac{5}{7}
\]

This is the equation of the line in slope-intercept form \( y = mx + b \).

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

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Here are 5 related questions to practice:

1. How do you derive the equation of a line using two given points?
2. What is the meaning of the slope in the context of a graph?
3. How do you convert a line's equation from standard form to slope-intercept form?
4. What happens to the graph of a line if the slope is positive instead of negative?
5. How can you determine the y-intercept by looking at a graph?

**Tip:** In point-slope form, the point you use doesn't have to be an intercept—it can be any point on the line.

Use the point-slope form to write an equation of the line. Write the equation in slope-intercept form.

Learn how to write the equation of a line using point-slope form and convert it to slope-intercept form. This problem involves a line with a slope of -1/7 passing through the point (-2, 1). Suitable for students in Grades 8-10.

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