To write the equation of the line in point-slope form, we need two key pieces of information:

1. The slope ($m$) of the line.
2. A point on the line, which is given as $(4, -7)$.

Step 1: Calculate the slope

To find the slope, we can identify two points on the line. The graph shows the line passing through the points:

• $(-4, 4)$
• $(4, -7)$

The slope $m$ is calculated by the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute the coordinates of the two points: $m = \frac{-7 - 4}{4 - (-4)} = \frac{-11}{8}$

Step 2: Use point-slope form

The point-slope form of a line's equation is: $y - y_1 = m(x - x_1)$ We use the point $(4, -7)$ and the slope $m = -\frac{11}{8}$: $y - (-7) = -\frac{11}{8}(x - 4)$ Simplify: $y + 7 = -\frac{11}{8}(x - 4)$

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

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:

1. How do you convert the point-slope form to slope-intercept form?
2. Can you calculate the slope if you are given only one point and the line's equation?
3. How would you write the equation if the slope were positive?
4. What does the slope represent in real-world applications?
5. How does the point-slope form differ from the general form of a line's equation?

Tip: Always check the coordinates carefully when calculating the slope to avoid sign mistakes!