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To solve for the **y-intercept** of the line passing through the points (2, 15) and (6, 39), we can use the slope-intercept form of a linear equation, which is:

\[
y = mx + b
\]

where:
- \( m \) is the slope,
- \( b \) is the **y-intercept**.

### Step 1: Find the slope (\(m\))

The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points (2, 15) and (6, 39):

\[
m = \frac{39 - 15}{6 - 2} = \frac{24}{4} = 6
\]

So, the slope \( m = 6 \).

### Step 2: Use the slope to find the y-intercept (\(b\))

Now, we use one of the given points and substitute it into the slope-intercept form to solve for \( b \). Using the point (2, 15):

\[
15 = 6(2) + b
\]

\[
15 = 12 + b
\]

\[
b = 15 - 12 = 3
\]

### Final Answer:
The **y-intercept** of the line is \( b = 3 \).

Would you like further details or clarification on any steps?

### 5 Related Questions:
1. How do you derive the equation of a line when only two points are given?
2. What is the significance of the slope in a linear equation?
3. How can you verify the equation of a line using other points on the line?
4. What happens if the slope between two points is zero?
5. How do you graph a line using its slope and y-intercept?

### Tip:
Always double-check your slope calculation, as it's the key to finding the correct equation of the line.

A straight line passes through the points (2, 15) and (6, 39). What is the y-intercept of the line?

Learn how to find the y-intercept of a straight line that passes through the points (2, 15) and (6, 39). This solution includes key concepts in coordinate geometry, such as the slope formula and slope-intercept form, and is suitable for Grades 8-10.

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