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

$y - y_1 = m(x - x_1)$

where $(x_1, y_1)$ is a point on the line, and $m$ is the slope.

Given:

• Point: $(x_1, y_1) = (5, -12)$
• Slope: $m = -\frac{2}{5}$

Substitute these values into the formula:

$y - (-12) = -\frac{2}{5}(x - 5)$

Simplify:

$y + 12 = -\frac{2}{5}(x - 5)$

The equation in point-slope form is:

$y + 12 = -\frac{2}{5}(x - 5)$

Graphing the Line

To graph this line, you could:

1. Start at the point $(5, -12)$.
2. Use the slope $-\frac{2}{5}$, which means move down 2 units and right 5 units to find another point.
3. Draw the line through these points.

Would you like more details, or do you have questions?

---

Related Questions:

1. What is the general form of a linear equation?
2. How do you convert from point-slope form to slope-intercept form?
3. What does the slope represent in a real-world context?
4. How do you graph a line given a point and a slope?
5. How can you check if a point lies on a given line?

Tip: In point-slope form, the point used does not have to be on the y-axis, making it very flexible for any point on the line.