Nolan plots the *y*-intercept of a line at (0, 3) on the *y*-axis. He uses a slope of 2 to graph another point. He draws a line through the two points. Which equation represents Nolan’s line?

*y* = 2*x* + 1

*y* = 2*x* + 3

*y* = 3*x* + 2

*y* = 3*x* + 5

To determine the equation of Nolan's line, we need to use the point-slope form of a line equation, which is given by the slope-intercept form:

\[
y = mx + b
\]

where:
- \( m \) is the slope of the line.
- \( b \) is the y-intercept of the line.

### Given Information:
- The y-intercept of the line is at \( (0, 3) \), so \( b = 3 \).
- The slope \( m = 2 \).

### Substituting into the Slope-Intercept Form:

\[
y = mx + b
\]

Substitute \( m = 2 \) and \( b = 3 \):

\[
y = 2x + 3
\]

### Conclusion:

The correct equation that represents Nolan’s line is:

\[
\boxed{y = 2x + 3}
\]

Would you like more details on this solution or have any other questions?

Here are 5 related questions to expand your understanding:
1. How would the equation change if the slope were negative?
2. What is the geometric interpretation of the slope in this context?
3. How can you find the x-intercept of a line given its equation?
4. How would the equation change if the y-intercept were at \( (0, -3) \) instead?
5. How do you graph a line given its slope and y-intercept?

**Tip:** The y-intercept (\(b\)) represents the point where the line crosses the y-axis, while the slope (\(m\)) indicates the steepness and direction of the line.

Learn how to graph Nolan's line using the slope-intercept form y = mx + b. Understand the relationship between the slope, y-intercept, and equation of a line through detailed explanation and examples. Suitable for Grades 7-9.

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