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.