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To find the equation of the line in **slope-intercept form** \( y = mx + b \), we need to determine two key components:

1. **Slope** (\( m \))
2. **y-intercept** (\( b \))

### Step 1: Find the Slope (\( m \))
The slope is calculated using two points on the line. The two points given on the graph are:
- \( (0, 7) \)
- \( (8, -2) \)

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

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

Substitute the points \( (0, 7) \) and \( (8, -2) \):

\[
m = \frac{-2 - 7}{8 - 0} = \frac{-9}{8}
\]

So, the slope \( m = -\frac{9}{8} \).

### Step 2: Find the y-Intercept (\( b \))
The y-intercept is the value of \( y \) when \( x = 0 \). From the point \( (0, 7) \), we can directly see that the y-intercept is \( b = 7 \).

### Final Equation
Now, we can write the equation of the line in slope-intercept form:

\[
y = -\frac{9}{8}x + 7
\]

This is the equation of the graphed line.

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Would you like any further details or explanations?

Here are 5 questions to deepen your understanding:
1. What does the slope of a line represent in geometry?
2. How would the equation change if the line passed through different points?
3. Can you calculate the slope of a vertical line?
4. What is the meaning of the y-intercept in a real-world context?
5. How would you convert this equation into standard form?

**Tip**: In slope-intercept form, the slope tells you how steep the line is, and the y-intercept shows where the line crosses the y-axis.

What is the equation of this graphed line?

Learn how to find the equation of a line passing through two points, (0,7) and (8,-2), using the slope-intercept form. The step-by-step solution involves calculating the slope and identifying the y-intercept. Suitable for students in Grades 8-10.

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