Use the point-slope form to write an equation of the line with the given properties.

Slope −7; passes through (−3, −7)Then write the equation in slope-intercept form.

To write the equation of a line using the point-slope form, we use the following formula:

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

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

Given:
- Slope \( m = -7 \)
- Point \( (x_1, y_1) = (-3, -7) \)

Substitute these values into the point-slope form:

\[
y - (-7) = -7(x - (-3))
\]
\[
y + 7 = -7(x + 3)
\]

Now, simplify and solve for \( y \) to get the equation in slope-intercept form:

\[
y + 7 = -7x - 21
\]
\[
y = -7x - 21 - 7
\]
\[
y = -7x - 28
\]

Thus, the equation in slope-intercept form is:

\[
y = -7x - 28
\]

### Summary:
- **Point-slope form**: \( y + 7 = -7(x + 3) \)
- **Slope-intercept form**: \( y = -7x - 28 \)

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Would you like more details on how these forms work or have any other questions?

Here are some related questions to further explore:

1. What is the standard form of the equation of a line?
2. How do you convert from point-slope form to standard form?
3. What are the steps for finding the slope between two points?
4. Can a vertical line be written in slope-intercept form?
5. How do you graph a line from its slope-intercept form?

**Tip:** Always remember that the slope-intercept form \( y = mx + b \) gives both the slope and the y-intercept directly.

Use the point-slope form to write an equation of the line with the given properties. Slope −7; passes through (−3, −7). Then write the equation in slope-intercept form.

Discover how to write the equation of a line with slope -7 passing through the point (-3, -7) using point-slope form and then convert it into slope-intercept form. This algebra problem explores key concepts of linear equations and is suitable for Grades 8-10.

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