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To find the equation of the linear function whose graph is shown, we need to determine two key elements:

1. **Slope (m)**: This measures the steepness and direction of the line.
2. **Y-intercept (b)**: This is the point where the line crosses the y-axis.

### Step 1: Identify Two Points on the Line
From the graph, we can identify two points:
- Point A: (2, 7)
- Point B: (-3, -2)

### Step 2: Calculate the Slope (m)
The slope formula is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points (2, 7) and (-3, -2):
\[
m = \frac{-2 - 7}{-3 - 2} = \frac{-9}{-5} = \frac{9}{5}
\]
The slope \( m = \frac{9}{5} \).

### Step 3: Find the Y-intercept (b)
We use the slope-intercept form of the equation:
\[
y = mx + b
\]
Substitute one of the points into the equation. Using point (2, 7):
\[
7 = \frac{9}{5}(2) + b
\]
\[
7 = \frac{18}{5} + b
\]
Subtract \(\frac{18}{5}\) from both sides to solve for \( b \):
\[
b = 7 - \frac{18}{5} = \frac{35}{5} - \frac{18}{5} = \frac{17}{5}
\]

### Final Equation
The equation of the line is:
\[
y = \frac{9}{5}x + \frac{17}{5}
\]

Would you like further details or have any questions?

Here are five related questions to expand your understanding:

1. How would the equation change if the slope was negative?
2. What does the y-intercept tell you about the graph of the line?
3. Can you find the x-intercept for this equation?
4. How would you write the equation in standard form \(Ax + By = C\)?
5. How do you find the slope if you know the angle of the line?

**Tip:** Always check the signs of your slope and y-intercept carefully; they indicate the direction and position of the line on the graph.

Find the equation of the linear function whose graph is given here. Use the letter x in your answer rather than the multiplication symbol.

Learn how to determine the equation of a linear function from a given graph by calculating the slope and intercept. This problem covers concepts like the slope formula and slope-intercept form. Suitable for students in Grades 8-10.

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