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To find the equation of the line from the graph and express it in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, follow these steps:

### 1. Identify the y-intercept (\( b \)):
Looking at the graph, the line crosses the y-axis at the point \( (0, -4) \). Therefore, the y-intercept is:
\[
b = -4
\]

### 2. Calculate the slope (\( m \)):
The slope \( m \) is calculated as the "rise over run," or:
\[
m = \frac{\Delta y}{\Delta x}
\]
From the graph, two points on the line are \( (0, -4) \) and \( (4, 2) \). The change in \( y \) (rise) is \( 2 - (-4) = 6 \), and the change in \( x \) (run) is \( 4 - 0 = 4 \). Therefore, the slope is:
\[
m = \frac{6}{4} = \frac{3}{2}
\]

### 3. Write the equation:
Substituting the values of \( m = \frac{3}{2} \) and \( b = -4 \) into the slope-intercept form, the equation of the line is:
\[
y = \frac{3}{2}x - 4
\]

### Summary:
- **Slope (m):** \( \frac{3}{2} \)
- **Y-intercept (b):** \( -4 \)

Would you like more details or have any questions?

Here are 5 related questions to expand this topic:
1. How can you find the slope of a line when given only two points?
2. What is the significance of the y-intercept in real-world scenarios?
3. Can you rewrite the equation \( y = \frac{3}{2}x - 4 \) in standard form \( Ax + By = C \)?
4. What happens to the graph of the line if the slope is negative?
5. How would you interpret the slope and y-intercept if this line represented a real-world situation, like cost versus time?

**Tip:** Always double-check points on the graph when calculating slope to ensure accuracy in rise over run!

Find the equation of the line graphed below. Write the equation in the form y = mx + b and identify m and b.

Learn how to find the equation of a line by using slope-intercept form y = mx + b. This solution includes finding the slope and y-intercept from a graph and applying the formula. Perfect for students in Grades 8-10.

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