Graphing Linear Equations

Objective Learn to recognize linear equations and to graph them by plotting points by hand.

The most important objective in this lesson is that you practice graphing lines by hand. This process is important because it helps increase your understanding of what the graphs mean and how the graphs depend on the coefficients in the linear equations.

The class of equations that have straight lines as graphs is called the class of linear equations, and that this class can be described algebraically.

Key Idea A linear equation can always be written in the form 2

Ax + By = C .

The equations 2x - 5y = 7, 3x + 5y = -1, and -4x + 7y = 11 are all linear equations.

Note that the form in the key idea is only one form in which linear equations may be expressed. Equations not in the Ax + By = C form are still linear because they can be rewritten in this form by using the Addition and Multiplication Properties of Equality. Besides, not all equations are given using the variables x and y. When other variables are used, it is important to specify which variable corresponds to the horizontal axis and which corresponds to the vertical axis.

The equation d = 3 t is linear. It can be rewritten as - 3t + d = 0 by subtracting 3t from each side of the equation. This equation is in the Ax + By = C form, with t playing the role of x and d playing the role of y .

The equation y = -4 x + 1 is linear. By adding 4x to each side, it can be rewritten as 4 x + y = 1.

For an equation in the Ax + By = C form, it is usually best to solve for y in terms of x in order to plot points.