Standard+Form

**Graphing Linear Functions-Target D: Graphing a linear equation from any form.**

 * STANDARD FORM** of a linear function is written as Ax + By = C, where the x and y terms are together on one side of the equals sign. There are two methods for graphing a line of a function from standard form. The x- and y-intercepts can be found from the equation and then graphed, or the equation can be converted into slope-intercept (function) form.

To find the x- and y-intercepts for any given equation, we substitute in zero. Why is that? Let's take a look at the graph below:
 * Method #1: Graphing from Standard Form by Identifying Intercepts**



What is the y-coordinate for each x-intercept? That's right, it's zero. So when you are trying to find the x-intercept from an equation, substitute zero in for y. What is the x-coordinate for each y-intercept? Right again, it's zero! When you are trying to find the y-intercept from an equation, substitute zero in for x.

Time to give it a try!

Example: Find the x- and y-intercepts of the line of the equation 2x - 6y = 12. Then graph the line.

To identify the x-intercept of the line of the equation 2x - 6y = 12, substitute zero in for the y-value and solve for x. Make sure to write the x-intercept as a coordinate!



To identify the y-intercept of the line of the equation 2x - 6y = 12, substitute zero in for the x-value and solve for y. Make sure to write the y-intercept as a coordinate!

In order to graph the line of the equation, plot both the x-intercept and y-intercept and draw the line through the points.

Sometimes graphing by finding the intercepts is not the best approach to graphing from standard form. Let's take a look at the equation: 3x - 5y = -10. The intercepts of this equation are (-10/3, 0) and (0, 2). Since the x-intercept is not an integer, it would be very difficult to accurately graph the line of this equation. So using Method #2 might be a better approach.

To convert an equation that is in standard form into slope-intercept form, you need to solve the equation for y.
 * Method #2: Graphing from Standard Form by Converting to Slope-Intercept Form**

Example: Graph the line of the equation 3x - 5y = -10.

First, convert the equation from standard form into function (slope-intercept) form.

Then, graph the line by plotting the y-intercept (0, 2), and then using the slope (m = 3/5) to plot as additional point.




 * Quick Check for Graphing in Standard Form:**

Graph the following linear equation in standard form. 1) 3x - 2y = 6

Quick Check Solutions - Graphing in Standard Form

Back to Graphing Linear Functions-Target D-Graph It-Guided Learning