The equation given is $y = -2x$, which is a linear equation with a slope of -2 and a y-intercept of 0. This means that the graph is a straight line passing through the origin (0, 0), and the slope tells us that for every 1 unit increase in $x$, $y$ decreases by 2 units.

Here’s how to plot the line on the graph:

1. Start at the origin (0, 0), since there is no y-intercept term (i.e., the constant term is 0).
2. Use the slope to find the next point. The slope $-2$ can be interpreted as "down 2 units for every 1 unit to the right." So from (0, 0), move 1 unit to the right (to $x = 1$) and then 2 units down (to $y = -2$). This gives the point (1, -2).
3. You can also move to the left. From the origin, move 1 unit to the left (to $x = -1$) and then 2 units up (to $y = 2$). This gives the point (-1, 2).
4. Draw a straight line through these points.

The line should pass through points such as (0, 0), (1, -2), and (-1, 2), and continue following the pattern established by the slope.

Would you like more details on how the slope affects the line or have any further questions?

Related questions:

1. How do you find the slope of a line given two points?
2. How would the graph change if the equation was $y = 2x$ instead?
3. What happens to the graph if you add a y-intercept, such as $y = -2x + 3$?
4. How do negative slopes affect the direction of a line compared to positive slopes?
5. Can you explain how to calculate the x-intercept of a linear equation?

Tip: The y-intercept is where the line crosses the y-axis, and the x-intercept is where the line crosses the x-axis. For $y = -2x$, the y-intercept is at (0, 0).