Question 2 Find the \( x \)-intercept and \( y \)-intercept of the graph of \( 2 x-2 y=-2 \). Then graph. \( x \)-intercept \( =(0,0) \)

Let's find the \( x \)-intercept and \( y \)-intercept of the equation \( 2x - 2y = -2 \), and then describe how to graph it. ### 1. Finding the Intercepts **a. \( x \)-intercept** The \( x \)-intercept occurs where the graph crosses the \( x \)-axis. At this point, the value of \( y \) is 0. Set \( y = 0 \) in the equation and solve for \( x \): \[ 2x - 2(0) = -2 \\ 2x = -2 \\ x = \frac{-2}{2} \\ x = -1 \] So, the \( x \)-intercept is **\( (-1,\ 0) \)**. **b. \( y \)-intercept** The \( y \)-intercept occurs where the graph crosses the \( y \)-axis. At this point, the value of \( x \) is 0. Set \( x = 0 \) in the equation and solve for \( y \): \[ 2(0) - 2y = -2 \\ -2y = -2 \\ y = \frac{-2}{-2} \\ y = 1 \] So, the \( y \)-intercept is **\( (0,\ 1) \)**. ### 2. Summary of Intercepts - **\( x \)-intercept**: \( (-1,\ 0) \) - **\( y \)-intercept**: \( (0,\ 1) \) > **Note:** Your original statement of the \( x \)-intercept as \( (0,\, 0) \) is incorrect. The correct \( x \)-intercept is \( (-1,\ 0) \). ### 3. Graphing the Equation To graph the equation \( 2x - 2y = -2 \): 1. **Plot the Intercepts**: - Plot the \( x \)-intercept at \( (-1, 0) \). - Plot the \( y \)-intercept at \( (0, 1) \). 2. **Draw the Line**: - Use a ruler to draw a straight line passing through the two intercepts. 3. **Extend the Line**: - Extend the line in both directions beyond the intercepts. 4. **Arrowheads**: - Add arrowheads to indicate that the line continues infinitely in both directions. 5. **Label the Line**: - Optionally, label the line with its equation \( 2x - 2y = -2 \). Here's a **diagrammatic representation**: ``` y | 2 | * 1 | | (0,1) 0 |--------*--------x (-1,0) ``` - The point \( (-1, 0) \) is the \( x \)-intercept. - The point \( (0, 1) \) is the \( y \)-intercept. - The line connecting these points represents the equation \( 2x - 2y = -2 \). ### 4. Alternative Form For easier graphing, you can rewrite the equation in **slope-intercept form** (\( y = mx + b \)): \[ 2x - 2y = -2 \\ -2y = -2x - 2 \\ y = x + 1 \] - **Slope (\( m \))**: 1 - **\( y \)-intercept (\( b \))**: 1 This form confirms the \( y \)-intercept at \( (0, 1) \) and makes it easy to plot additional points if needed.