
Write an equation in point-slope form of the line that passes through 2 points;
(3, 4) & (-6, 7). 

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.

Write an equation in point-slope form of the line that passes through 2 points; (3, 4) & (-6, 7).

Learn how to write the equation of a line in point-slope form that passes through the points (3, 4) and (-6, 7). This solution explains how to calculate the slope and use the point-slope form equation. Suitable for students in Grades 8-10.

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