A linear equation is almost like any other equation, with two expressions set equal to each other. Linear equations have one or two variables. When substituting values for the variables in a true linear equation and graphing the coordinates, all correct points lie on the same line. For a simple slope-intercept linear equation, one must determine the slope and the y-intercept first. Use a line already drawn on a graph and its demonstrated points before creating a linear equation.
Follow this formula in making slope-intercept linear equations: y = mx + b. Determine the value of m, which is the slope (rise over run). Find the slope by finding any two points on a line. For this example, use points (1,4) and (2,6). Subtract the x value of the first point from the x value of the second point. Do the same for the y values. Divide these values to get your slope.
Example: (6-4) / (2/1) = 2 / 1 = 2
The slope, or m, equals 2. Substitute 2 for m in the equation, so it should now look like this: y = 2x + b.
Find a point on the line and substitute the values into your equation. For example, for the point (1,4), use the x and y values in the equation to get 4 = 2(1) + b.
Solve the equation and determine the value of b, or the value at which the line intersects the x-axis. In this case, subtract the multiplied slope and x value from the y value. The final solution is y = 2x + 2.