Graph this line using the slope and \( y \)-intercept: \[ y=2 x+4 \]

To graph the line \( y = 2x + 4 \) using the slope and \( y \)-intercept, follow these steps: ### 1. Identify the \( y \)-Intercept The equation \( y = 2x + 4 \) is in the slope-intercept form \( y = mx + b \), where: - \( m \) is the **slope**. - \( b \) is the **\( y \)-intercept**. Here, the \( y \)-intercept \( b = 4 \). This means the line crosses the \( y \)-axis at the point **(0, 4)**. ### 2. Determine the Slope The slope \( m = 2 \) indicates the steepness and direction of the line. A slope of 2 means that for every **1 unit** you move **horizontally** (to the right), you move **2 units** **vertically** (upward). ### 3. Plot the \( y \)-Intercept Start by plotting the point **(0, 4)** on the coordinate plane. ### 4. Use the Slope to Find Another Point From the \( y \)-intercept: - Move **1 unit to the right** (increase \( x \) by 1). - Move **2 units up** (increase \( y \) by 2). This takes you to the point **(1, 6)**. ### 5. Draw the Line Use a ruler to draw a straight line passing through the points **(0, 4)** and **(1, 6)**. Extend the line in both directions and add arrowheads to indicate that it continues indefinitely. ### 6. (Optional) Add Another Point for Accuracy To ensure accuracy, you can plot a third point using the slope: - From **(1, 6)**, move **1 unit to the right** to \( x = 2 \). - Move **2 units up** to \( y = 8 \), giving the point **(2, 8)**. ### Visual Representation Here's a simple ASCII representation of the graph: ``` y | 10 | 9 | 8 | * (2,8) 7 | 6 | * (1,6) 5 | 4 | * (0,4) 3 | 2 | 1 | 0 |-------------------------- 0 1 2 3 4 x ``` - The asterisks (*) represent the points plotted. - Draw a straight line through these points to represent \( y = 2x + 4 \). ### Summary - **\( y \)-Intercept**: (0, 4) - **Slope**: 2 (rise over run: up 2, right 1) - **Additional Points**: (1, 6), (2, 8), etc. - **Graph**: A straight line passing through these points, rising upward as \( x \) increases. By following these steps, you can accurately graph the line \( y = 2x + 4 \) on a coordinate plane.