The simplest way to graph a line is by plotting points. In this method, you plot several individual points on a graph and connect them with a line. You need to plot a minimum of two points to graph using this method. The easiest two points to graph are the y-intercept, which is the point where the line crosses the y-axis, and the x-intercept, where the line crosses the x-axis.
To plot the x-intercept, change the "y" in your linear equation to 0 and solve for "x." Plot a point at the corresponding location on the y-axis. To plot the y-intercept, change the "x" in your linear equation to 0 and solve for "y." Plot a point at the corresponding location on the x-axis. Use a ruler or other straightedge to connect the two points with a line.
Suppose you are given the equation 3x + 2y = 6. To find the x-intercept, substitute 0 for y, forming the equation 3x + 2(0) = 6, or simply 3x = 6. Divide both sides of the equation by 3 to get x = 2. Plot the point at (2, 0). To find the y-intercept for 3x + 2y = 6, you substitute 0 for x, giving you the equation 3(0) + 2y = 6, or simply 2y = 6. Divide both sides of the equation by 2 to get y = 3. Plot the point at (0, 3).
This method is faster than the plotting-points method, but it requires you to have a linear equation in slope-intercept form. Slope-intercept form is y = mx + b. If your equation is not in this form, you can try to convert it or use the plotting points method instead. Remember that when converting that you can add, subtract, multiply or divide the equation by any number, as long as you perform the operation to both sides of the equal sign.
In the y = mx + b equation, "b" is the y-intercept. Plot a point at (0, b). "M" is the slope, which determines how steep the line is. For example, a slope of 1 rises one unit for each unit to the right. A slope of 2 rises two units up for each unit to the right. A slope of 1/2 rises one unit up for every two units to the right. Negative slopes descend; for example, a slope of -2 descends two units for each unit to the right.
Suppose you are given the equation 2x + 3y = 9, which is in standard form. You need to convert it to slope-intercept form first before graphing it. First, subtract 2x from both sides, forming 3y = -2x + 9. Next, divide both sides of the equation by 3, forming y = -2/3x + 3. You now have an equation in slope-intercept form where the slope is -2/3 and the y-intercept is 3. Plot the y-intercept at (0, 3). Because the slope is -2/3, you need to plot the point two units down and three to the right, which is at (3, 1). Continue plotting points, using the slope as your guide, until you have enough points to form a line.