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.