A line has a slope of

–

3

5

and passes through the point

(

–

4

,

–

6

)

.

What is its equation in point-slope form?

To find the equation of a line in **point-slope form**, we use the formula:

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

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

Given:
- The slope \( m = -\frac{3}{5} \)
- The point \( (-4, -6) \)

Substitute these values into the point-slope formula:

\[
y - (-6) = -\frac{3}{5}(x - (-4))
\]

Simplifying the double negatives:

\[
y + 6 = -\frac{3}{5}(x + 4)
\]

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

Would you like more details on how to proceed further or graph this line?

---

Here are 5 related questions:
1. How would you convert this equation to slope-intercept form?
2. What is the y-intercept of the line based on the given information?
3. How do you find the x-intercept of the line?
4. What does the negative slope indicate about the line’s direction?
5. Can you use the point-slope form for vertical or horizontal lines?

**Tip:** The point-slope form is particularly useful for finding the equation of a line when you're given a point and the slope directly.

A line has a slope of -3/5 and passes through the point (-4, -6). What is its equation in point-slope form?

Find the point-slope form equation of a line with a slope of -3/5 passing through the point (-4, -6). This solution uses the point-slope formula to create a linear equation and is suitable for students in Grades 8-10.

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