Final answer:
To draw y = x on a graph, draw two perpendicular axes, label them, choose a scale, plot several points where x and y have equal values, and then connect these points with a straight line.
Step-by-step explanation:
To draw y = x on a graph, you begin by understanding that this is an equation of a line where for every point on the line, the value of y is equal to the value of x. Follow these steps to plot the line:
- Start by drawing two perpendicular axes, with the horizontal axis representing the independent variable (x) and the vertical axis representing the dependent variable (y).
- Label each axis accordingly, typically x for the horizontal and y for the vertical. Decide on a scale for both axes that will comfortably fit the data you intend to plot. For the equation y = x, the scales for both axes should be the same since y and x increase at the same rate.
- Plot a series of points where the x-value and the y-value are equal, for example, (0,0), (1,1), (2,2), and so forth. You can also use negative values like (-1,-1), (-2,-2), if necessary.
- Once you have plotted several points, draw a straight line through them which should cut equally across both the x and y axis.
The line y = x is a straight line that forms a 45-degree angle with both the x-axis and y-axis because it has a slope of 1 (rise over run is 1/1).