what is the point-slope form of the line with slope 2/5 that passes through the point (-4,-7)

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

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

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

For the given problem:
- The slope \( m = \frac{2}{5} \),
- The point \( (-4, -7) \).

Substituting these values into the point-slope formula:

\[
y - (-7) = \frac{2}{5}(x - (-4))
\]

Simplifying the equation:

\[
y + 7 = \frac{2}{5}(x + 4)
\]

This is the point-slope form of the line.

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. How would you convert this point-slope form to slope-intercept form?
2. What is the equation of a line with a slope of 3 that passes through the point (1, 2)?
3. How can you determine if two lines are parallel?
4. What is the distance between the points (-4, -7) and (2, 3)?
5. How do you find the slope given two points?

**Tip:** Point-slope form is particularly useful when you know the slope and any point on the line, not just the y-intercept.

Learn how to find the point-slope form of a line with a slope of 2/5 passing through the point (-4, -7). This problem covers key algebraic concepts and demonstrates the application of the point-slope formula in solving linear equations. Suitable for students in Grades 8-10.

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