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

### Step 1: Identify two points on the line
From the graph, I can see two clear points that the line passes through:
- Point 1: \( (0, -24) \) (the y-intercept)
- Point 2: \( (6, 6) \)

### Step 2: Calculate the slope \( m \)
The slope \( m \) is given by the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \( (0, -24) \) and \( (6, 6) \):
\[
m = \frac{6 - (-24)}{6 - 0} = \frac{6 + 24}{6} = \frac{30}{6} = 5
\]

### Step 3: Find the y-intercept \( b \)
From the graph, we already know that the y-intercept is \( -24 \) since the line crosses the y-axis at \( (0, -24) \).

### Step 4: Write the equation
Using the slope \( m = 5 \) and y-intercept \( b = -24 \), the equation of the line is:
\[
y = 5x - 24
\]

Would you like more details or have any questions?

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Here are 5 related questions:
1. How do you find the slope if the points are fractions or decimals?
2. What does the slope of a line represent in real-world problems?
3. Can the slope-intercept form be used for vertical and horizontal lines?
4. How would you rewrite this equation in standard form?
5. How can you use this equation to predict values of \( y \) for different \( x \)-values?

**Tip:** Always ensure that the two points you choose from the graph are accurately identified for correct slope calculation.

Write the equation of this line in slope-intercept form based on the provided graph.

Learn how to determine the equation of a line from a graph using slope-intercept form. This example features a detailed step-by-step solution, including slope calculation and identification of the y-intercept. Suitable for students in Grades 7-9.

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