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Let's find the equation of the line in the form \( y = mx + b \), where:

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

### Step 1: Determine the slope (\( m \))
The slope formula is:
\[
m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}
\]
From the graph, we can pick two points on the line. Let's use the points \( (0, -3) \) and \( (3, 3) \).

- The rise between these points is \( 3 - (-3) = 6 \).
- The run is \( 3 - 0 = 3 \).

Thus, the slope is:
\[
m = \frac{6}{3} = 2
\]

### Step 2: Determine the y-intercept (\( b \))
The y-intercept is where the line crosses the y-axis. From the graph, we see that the line crosses the y-axis at \( (0, -3) \). Therefore, \( b = -3 \).

### Final Equation
The equation of the line is:
\[
y = 2x - 3
\]

Would you like further clarification or additional details on this? 

Here are 5 related questions for practice:
1. What is the slope of a line passing through points \( (2, 3) \) and \( (5, 7) \)?
2. How do you find the x-intercept of a line given its equation?
3. How do you calculate the slope if you're given a horizontal line?
4. What is the equation of a line parallel to \( y = 2x - 3 \) but passing through \( (1, 4) \)?
5. How does the graph of \( y = mx + b \) change when you modify \( m \) or \( b \)?

**Tip:** When choosing points on a graph to calculate the slope, use points that lie exactly at grid intersections for greater accuracy.

Find an equation y = mx + b for the line whose graph is sketched.

Learn how to find the equation of a line in slope-intercept form, y = mx + b, based on a graph. This example involves calculating the slope and determining the y-intercept, essential for understanding linear equations in algebra. Suitable for students in Grades 8-10.

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