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.