Use point-slope form to write the equation of a line that passes through the point left parenthesis, 6, comma, 7, right parenthesis(6,7) with slope minus, 3−3.

The point-slope form of a line is given by the formula:

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

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

Given:
- Point: \( (6, 7) \),
- Slope: \( -3 \),

we substitute these values into the formula:

\[
y - 7 = -3(x - 6)
\]

This is the equation of the line in point-slope form.

If you'd like, we can expand it to the slope-intercept form (\( y = mx + b \)).

Do you want further details or have any questions?

Here are 5 related questions:
1. How can we convert this equation into slope-intercept form?
2. What is the slope-intercept form of a line, and how does it relate to point-slope form?
3. How do we graph the line using the point \( (6, 7) \) and the slope \( -3 \)?
4. How do we find the x-intercept and y-intercept from this equation?
5. Can we use a different point on the line to write the equation again in point-slope form?

**Tip:** The point-slope form is especially useful when you know the slope and one point on the line, as it avoids having to find the y-intercept directly.

Use point-slope form to write the equation of a line that passes through the point (6, 7) with slope -3.

Learn how to use the point-slope form to write the equation of a line passing through the point (6, 7) with a slope of -3. This problem introduces key algebraic concepts related to linear equations and the point-slope formula. Suitable for students in Grades 8-10.

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