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The x-intercept is where a graph crosses the x-axis. This is an important point because it shows where the value of the function is zero along the y-axis. To find the x-intercept of an equation, we set the value of \( y \) to zero and solve for \( x \). In our exercise, the equation given is:\[ \frac{1}{2} x + \frac{1}{2} y = -1 \]By substituting \( y = 0 \), the equation simplifies to:\[ \frac{1}{2} x + \frac{1}{2} \times 0 = -1 \]This reduces to:\[ \frac{1}{2} x = -1 \]Multiplying both sides by 2 gives us \( x = -2 \). Therefore, the x-intercept is the point \( (-2, 0) \).

• Set \( y = 0 \).
• Solve the simplified equation for \( x \).

Understanding this helps visualize part of the graph on the x-axis where it starts or ends crossing.

The y-intercept is where the graph touches the y-axis. Similar to the x-intercept, the y-intercept shows the point at which the value of \( x \) is zero. It's an essential part of sketching the graph because it indicates the start or end point along the y-axis. To find the y-intercept, we set \( x = 0 \) in our equation:\[ \frac{1}{2} x + \frac{1}{2} y = -1 \]Substituting \( x = 0 \), the equation becomes:\[ \frac{1}{2} \times 0 + \frac{1}{2} y = -1 \]This simplifies to:\[ \frac{1}{2} y = -1 \]Multiplying both sides by 2 results in \( y = -2 \). Hence, the y-intercept is at the point \( (0, -2) \).

• Set \( x = 0 \).
• Solve the simplified equation for \( y \).

Locating the y-intercept gives us another crucial point on the graph, determining where it crosses the y-axis.

Graphing lines involves plotting points and drawing straight lines through them. For equations like \[ \frac{1}{2} x + \frac{1}{2} y = -1 \]we use the intercepts found: the x-intercept \( (-2, 0) \) and the y-intercept \( (0, -2) \). By plotting these points on a coordinate plane, we can draw a straight line through them.### Steps for Graphing1. **Identify Points:** - Use the intercepts as the primary points. - Optionally, choose extra points if needed for accuracy.
2. **Plot Points:** - Mark \( (-2, 0) \) and \( (0, -2) \) on the graph.
3. **Draw a Line:** - Use a ruler to connect the plotted points. - Extend the line across the graph if needed.### Understanding the Line- The line represents every possible solution to the equation.- It visually shows the relationship between \( x \) and \( y \) for the equation.- Wherever the line crosses the axes reflects the intercepts as calculated.Graphing this line means illustrating how any value of \( x \) will correlate to a value of \( y \), based on the equation, connecting numbers and visualization.