To graph the proportional relationship \( y = -2x \), we can create a table of values by choosing various values for \( x \) and calculating the corresponding \( y \) values. Then, we can plot these points on a coordinate plane.
Step 1: Create a Table of Points
| \( x \) | \( y = -2x \) | |:---------:|:---------------:| | -2 | 4 | | -1 | 2 | | 0 | 0 | | 1 | -2 | | 2 | -4 |
Step 2: Plot the Points
Now let's plot the points from the table on a coordinate system:
- Point (-2, 4)
- Point (-1, 2)
- Point (0, 0)
- Point (1, -2)
- Point (2, -4)
Step 3: Draw the Line
After plotting the points, we can draw a straight line through them because this is a linear function. The line will slope downward from the left to the right due to the negative coefficient of \( x \).
Graph Visualization
Although I cannot physically draw, the overall slope and intercept can be described:
- The line intercepts the origin (0, 0).
- The slope of the line is -2, indicating that for every 1 unit increase in \( x \), \( y \) decreases by 2 units.
You can use graphing software or graph paper to sketch this accurately. Just remember to connect the points with a straight line, extending it in both directions.
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