Linear Equations

Linear equations are probably the most commonly encountered type of equation in applied mathematics. Luckily, they are quite easy to deal with.

Linear equations have the standard form Ax + By = C. where A, B, and C are constants. Actually, a linear equation can have any number of variables, but the waiver exam will probably only test equations in two variables. Standard form is usually the easiest format to deal with when solving systems of equations, particularly when computer linear algebra software is being employed.

Linear equations are frequently rearranged into the so-called slope-intercept form: y = Mx + B. This form is easy to graph because M is equal to the slope of the line (change in y over change in x) and B is equal to the y-intercept.

Point-intercept form is useful for coming up with the equation of a line when you know two points. It has the format:

(y - y0) = (y1 - y0)/(x1 - x0) * (x - x1)

Where (x0, y0) and (x1, y1) are any two known points on the line.


Sources

Beecher, J., Penna, J., & Bittenger, M. (2008). College Algebra [3rd Ed.]. Boston, MA: Pearson.



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