Graph the line with the equation \( y=-x-2 \)

To graph the line \( y = -x - 2 \), follow these steps: ### 1. **Understand the Equation** The equation \( y = -x - 2 \) is in **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. For \( y = -x - 2 \): - **Slope (\( m \))**: -1 - **Y-intercept (\( b \))**: -2 ### 2. **Plot the Y-Intercept** Start by plotting the y-intercept on the graph. - **Point**: (0, -2)  ### 3. **Use the Slope to Find Another Point** The slope \( m = -1 \) means that for every 1 unit increase in \( x \), \( y \) decreases by 1 unit. - **Starting Point**: (0, -2) - **Move Right by 1** (increase \( x \) by 1): \( x = 1 \) - **Move Down by 1** (decrease \( y \) by 1): \( y = -3 \) - **Second Point**: (1, -3) ### 4. **Plot the Second Point** Plot the point (1, -3) on the graph.  ### 5. **Draw the Line** Connect the two points with a straight line, and extend it in both directions. ### 6. **Complete Graph** Here's the complete graph of the line \( y = -x - 2 \):  ### 7. **Graph Representation** If you're unable to view the images, here's a simple text-based representation: ``` y | 3 | 2 | 1 | 0 |---------●----- -1| / -2|●-----/ -3| ● -4| ------------------ x -2 -1 0 1 2 ``` - **Point (0, -2)**: Where the line crosses the y-axis. - **Point (1, -3)**: Another point on the line derived from the slope. ### 8. **Key Characteristics** - **Slope (\( m = -1 \))**: The line decreases by 1 unit vertically for every 1 unit it moves horizontally to the right. - **Y-Intercept (\( b = -2 \))**: The line crosses the y-axis at (0, -2). - **X-Intercept**: To find where the line crosses the x-axis (\( y = 0 \)): \[ 0 = -x - 2 \\ x = -2 \] So, the x-intercept is (-2, 0). ### 9. **Final Points to Plot** - **Y-Intercept**: (0, -2) - **X-Intercept**: (-2, 0) - **Additional Point**: (1, -3) Using these points, you can accurately draw the line \( y = -x - 2 \) on a coordinate plane.