Given the equation below, find the slope, \( y \)-intercept, and graph the lir \( y=\frac{1}{6} x-3 \) Slope \( (m): \square \) \( y \)-intercept (b):

Sure! Let's analyze the equation and extract the necessary information: ### Given Equation: \[ y = \frac{1}{6}x - 3 \] This equation is in the **slope-intercept form**, which is: \[ y = mx + b \] where: - \( m \) is the **slope** of the line. - \( b \) is the **\( y \)-intercept** (the point where the line crosses the \( y \)-axis). ### 1. Identifying the Slope and \( y \)-Intercept - **Slope (\( m \)):** \[ m = \frac{1}{6} \] - **\( y \)-Intercept (\( b \)):** \[ b = -3 \] So, filling in the blanks: - **Slope \( (m): \)** \( \frac{1}{6} \) - **\( y \)-intercept \( (b): \)** \( -3 \) ### 2. Graphing the Line To graph the line \( y = \frac{1}{6}x - 3 \), follow these steps: 1. **Plot the \( y \)-Intercept:** - Start at the point \( (0, -3) \) on the \( y \)-axis. 2. **Use the Slope to Find Another Point:** - The slope \( \frac{1}{6} \) means "rise over run," which is \( 1 \) unit up for every \( 6 \) units to the right. - From \( (0, -3) \), move **6 units to the right** to \( x = 6 \), and then **1 unit up** to \( y = -2 \). - Plot the second point at \( (6, -2) \). 3. **Draw the Line:** - Connect the two points with a straight line extending in both directions. ### Visual Representation: While I can't provide a graphical plot here, here's a simple sketch of how the line would appear: ``` y | 5 | 4 | 3 | 2 | • (6, -2) 1 | 0 |____________________________ x -1| -2| -3|• (0, -3) -4| -5| ``` - **Point (0, -3):** Where the line crosses the \( y \)-axis. - **Point (6, -2):** Another point on the line based on the slope. - The line extends infinitely in both directions through these points. ### Summary - **Slope \( (m) \):** \( \frac{1}{6} \) - **\( y \)-Intercept \( (b) \):** \( -3 \) This means the line rises gently as it moves from left to right, crossing the \( y \)-axis at \( -3 \).