How to Create Linear Equations

By Jane McDonaugh
Using imaginary numbers, you can find the solution to a quadratic that lacks an x-intercept.
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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.

About the Author

Jane McDonaugh has been a professional writer and editor since 2010, with expertise in literature, television, film and humor. She is a freelance reader for Author Solutions Film and has held many other positions in television and film production. McDonaugh holds a Bachelor of Arts in television production and English from Emerson College.