The graph of the direct variation equation y = 2x is a straight line passing through the origin with a slope of 2. As x increases or decreases, y changes proportionally, showcasing a direct variation relationship.
A direct variation equation is of the form y = kx, where k is the constant of variation. In the given equation y = 2x, the constant of variation is k = 2.
To graph the equation y = 2x, you can use the following steps:
1. Plot Points:
- Choose values for x and find the corresponding y values using the equation.
- For example, if x = 1, then y = 2(1) = 2. If x = -1, then y = 2(-1) = -2.
- Choose a few more values to get a set of points.
2. Plot the Points on a Coordinate Plane:
- Place points (1, 2), (-1, -2), (2, 4), (-2, -4), etc., on the coordinate plane.
3. Draw a Line:
- Since it's a direct variation, the graph is a straight line passing through the origin (0, 0).
- Connect the plotted points with a straight line.
The resulting graph is a line with a slope of 2, passing through the origin, representing the direct variation y = 2x.