What is the equation of the line that passes through the point left parenthesis, minus, 3, comma, 2, right parenthesis(−3,2) and has a slope of minus, 3−3?

The equation of a line can be written in **point-slope form** as:

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

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

You are given:
- Slope \(m = -3\),
- A point on the line \((-3, 2)\).

Substitute these values into the point-slope form:

\[
y - 2 = -3(x - (-3)) 
\]
\[
y - 2 = -3(x + 3)
\]

Now, simplify:

\[
y - 2 = -3x - 9
\]
\[
y = -3x - 9 + 2
\]
\[
y = -3x - 7
\]

Thus, the equation of the line is:

\[
y = -3x - 7
\]

### Do you want more details or have any questions about this? Here are some related questions:

1. How do you convert point-slope form to slope-intercept form?
2. What is the significance of the slope in a linear equation?
3. How do you find the slope between two points?
4. Can a line have an undefined slope? If so, what does that mean geometrically?
5. How would the equation change if the point was different, but the slope stayed the same?

**Tip:** Always remember that the slope \(m\) represents how steep the line is, and a negative slope means the line is decreasing as you move to the right.

What is the equation of the line that passes through the point (-3, 2) and has a slope of -3?

Learn how to determine the equation of a line passing through the point (-3, 2) with a slope of -3. This step-by-step solution covers key algebraic concepts such as the point-slope and slope-intercept forms of a linear equation. Suitable for students in Grades 8-10.

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