To graph the direct variation equation y=2x, plot the origin (0,0), find and plot additional points by selecting x-values and applying the slope, and then draw a straight line through all the points.
Graphing a Direct Variation Equation
To graph the direct variation equation y=2x, we begin by recognizing that this is a linear equation in the form of y = mx, where m is the slope of the line. In this case, the slope (m) is 2, and there is no y-intercept, meaning b is 0 and the line passes through the origin (0,0). Graphing this equation requires plotting the straight line that increases by two units in the y-direction for every one unit increase in the x-direction.
Here's how to graph this equation step-by-step:
Plot the origin point (0,0) because direct variation equations always pass through the origin.
Pick a value for x, such as 1, then multiply it by the slope to find the corresponding y value; for x=1, y would be 2 (since 2*1=2).
Plot the point (1,2) on the graph.
Repeat the previous step with a different x value, for example -1, to find another point; for x=-1, y would be -2.
Plot the second point (-1,-2).
Draw a straight line through the plotted points; this line is the graph of the equation y=2x.
Keep in mind that any direct variation line will always be a straight line passing through the origin, and the slope indicates how steep the line is.