Graph the proportional relationship y=−2x by plotting points

Answer 1

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.