Graphs, Functions, and Models

Graphing Linear Equations

Linear equations are equations of the form Ax + By = C, where A, B, and C are constants. The graph of a linear equation is always a straight line.

• Standard Form:

• Slope-Intercept Form: , where m is the slope and b is the y-intercept.

Finding Intercepts

• x-intercept: Set and solve for .

• y-intercept: Set and solve for .

Example: Find the x- and y-intercepts of the equation .

• x-intercept: Set :

• y-intercept: Set :

So, the x-intercept is and the y-intercept is .

Graphing Using Intercepts

1. Plot the x-intercept on the x-axis.

2. Plot the y-intercept on the y-axis.

3. Draw a straight line through these two points to graph the equation.

Additional info: This method is efficient for graphing linear equations in standard form, especially when the intercepts are integers.