Final answer:
The graph of y=2x is a straight line with a slope of 2, which means for every increase of 1 in x, y increases by 2. To plot it, calculate y values for chosen x values, plot the points, and draw the straight line through them.
Step-by-step explanation:
The graph of the equation y = 2x represents a straight line. To plot this line, you would start by choosing several values for x and then calculate the corresponding y values by applying the equation. For instance, if x is 0, then y would be (2)(0) = 0. If x is 1, then y would be (2)(1) = 2. The points that could be plotted on the graph are (0, 0), (1, 2), and other points found by repeating this process with different x values.
The graph would be represented on a Cartesian coordinate system where the horizontal axis (x-axis) is the independent variable and the vertical axis (y-axis) is the dependent variable. Since the equation does not have a b term, it means the line crosses the origin (0,0). The slope (m) of the line is 2, meaning the line rises 2 units vertically for every 1 unit it moves horizontally.
Plotting Data Pairs
To better understand the concept, if we had a different equation like y = x² + 2, plotting data pairs would also involve calculating the y values based on chosen x values and then plotting the resultant points to create a graphical representation of the equation.
Graphing a Straight-Line
However, for the linear equation y = 2x, the graph would be a straight line without curvature as indicated by the power of x being 1 (as opposed to x² which would produce a parabola). This line shows the direct dependence of y on x.