To write the equation of a line in point-slope form, we first need to determine the slope of the line passing through the points $(3, 4)$ and $(-6, 7)$.

Step 1: Calculate the slope (m)

The formula for the slope is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute the given points: $m = \frac{7 - 4}{-6 - 3} = \frac{3}{-9} = -\frac{1}{3}$

Step 2: Use the point-slope form equation

The point-slope form of a line is:

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

Using the slope $m = -\frac{1}{3}$ and one of the points, say $(3, 4)$, we substitute these values into the equation:

$y - 4 = -\frac{1}{3}(x - 3)$

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

Would you like further details or have any questions?

Here are 5 related questions:

1. How do you convert this equation into slope-intercept form?
2. Can the other point $(-6, 7)$ be used to write the equation in point-slope form?
3. How do you check if a point lies on a line given its equation?
4. What is the relationship between the slope and the angle of inclination of a line?
5. How do parallel lines relate in terms of slope?

Tip: In point-slope form, you can use any point on the line, not just one particular point.