Give the slope and \( y \)-intercept of the line whose equation is given. Then graph the linear function. \( f(x)=\frac{2}{5} x-8 \) A. The slope is (Simplify your answer. Type an integer or correct choice below and, if necessary, fill in a fraction.) B. The slope is undefined. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The y-intercept is (Simplify your answer. Type an integer or a fraction.) B. There is no \( y \)-intercept.

Let's analyze the linear function \( f(x) = \frac{2}{5}x - 8 \). ### A. The Slope The general form of a linear equation is: \[ f(x) = mx + b \] where: - \( m \) is the **slope**, - \( b \) is the **y-intercept**. For the given function: \[ f(x) = \frac{2}{5}x - 8 \] **Slope (\( m \))**: \[ m = \frac{2}{5} \] **Answer:** **A.** The slope is \( \frac{2}{5} \). ### B. The Y-Intercept Using the same general form: \[ f(x) = mx + b \] The **y-intercept (\( b \))** is the constant term in the equation. For the given function: \[ b = -8 \] **Answer:** **B.** The y-intercept is \( -8 \). ### Graphing the Linear Function To graph \( f(x) = \frac{2}{5}x - 8 \): 1. **Plot the Y-Intercept**: - Start by plotting the y-intercept at \( (0, -8) \). 2. **Use the Slope to Find Another Point**: - The slope \( \frac{2}{5} \) means that for every 5 units you move horizontally (to the right), you move 2 units vertically (up). - Starting from \( (0, -8) \), move 5 units to the right to \( x = 5 \) and 2 units up to \( y = -6 \). - Plot the second point at \( (5, -6) \). 3. **Draw the Line**: - Draw a straight line passing through the points \( (0, -8) \) and \( (5, -6) \). **Graph:** Since I can't draw the graph here, here's a description: - **Y-Intercept**: Point at \( (0, -8) \). - **Another Point**: Point at \( (5, -6) \). - **Line**: Draw a straight line through these points extending infinitely in both directions. ### Summary - **Slope:** \( \frac{2}{5} \) - **Y-Intercept:** \( -8 \)