Graphing Linear Equations and Finding Intercepts

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: $Ax + By = C$

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

Finding Intercepts

• x-intercept: Set $y = 0$ and solve for $x$.

• y-intercept: Set $x = 0$ and solve for $y$.

Example: Find the x- and y-intercepts of the equation $4x + 3y = 12$.

• x-intercept: Set $y = 0$:

$4x + 3(0) = 12$ $4x = 12$ $x = 3$

• y-intercept: Set $x = 0$:

$4(0) + 3y = 12$ $3y = 12$ $y = 4$

So, the x-intercept is $(3, 0)$ and the y-intercept is $(0, 4)$.

Graphing Using Intercepts

1. Plot the x-intercept $(3, 0)$ on the x-axis.

2. Plot the y-intercept $(0, 4)$ 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.