Write down the linear equation in slope-intercept form. For this example, let the equation be y = 2x - 4.
Set the x-variable to 0 and solve for y to calculate the y-intercept. For this example, y = 2 * (0) - 4 becomes y = -4 --- the y-intercept's coordinates are (0, -4).
Set the y-variable to 0 and solve for x to calculate the x-intercept. For this example, 0 = 2x - 4 becomes 2x = 4 and x = 2 --- the x-intercept's coordinates are (2, 0).
Substitute a value for the x-variable and solve for y to calculate a third point. In this example, substituting the value 3 for x results in y = 2 * 3 - 4, which results in y = 2 --- the third point is (3, 2).
Plot the y-intercept on the y-axis. The value of the y-intercept indicates how many places from the x-axis the point will be, and the sign of the y-intercept indicates if it is above or below the x-axis --- positive is above and negative is below. For this example, the y-intercept is -4, which means it is four places below the x-axis.
Plot the x-intercept on the x-axis. The x-intercept's value indicates how many places from the y-axis the point will be, and the sign of the x-intercept indicates if it is to the right or to the left of the y-axis --- positive is to the right, and negative is to the left. For this example, the x-intercept is 2, which means it is two places to the right of the y-axis.
Plot the third point with its x- and y-coordinates. As with the intercepts, the x-coordinate follows the rules of the x-intercept and the y-coordinate follows the rules of the y-intercept. The point combines those rules, with the point being both a specified distance from the x- and y-axes. For this example, the point (3, 2) is three places to the right of the y-axis and 2 points above the x-axis. To help imagine it, think of a line running parallel to the y-axis three spaces over and a line running parallel to the x-axis two spaces above --- the point is where those two imaginary lines intersect.
Connect the three points together by drawing a line with the straight edge of a ruler. Add arrows to either end of the line to signify that the line travels infinitely in both directions.