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Method

Graphing a Linear Function in Standard Form

A linear function written in standard form has quickly identifiable x- and y-intercepts. Since two points determine a line, this provides enough information to graph the function. Consider the following linear equation written in standard form. 3x+5y=30 The graph of this function can be drawn in two steps.

Find the Intercepts

Begin by substituting y= 0 to find the x-intercept of the equation.

3x+5y=30

Substitute

y= 0

3x+5( 0)=30

▼

Solve for x

ZeroPropMult

Zero Property of Multiplication

3x+0=30

IdPropAdd

Identity Property of Addition

3x = 30

DivEqn

.LHS /3.=.RHS /3.

x = 10

The x-intercept is (10,0). The y-intercept can be found in a similar way. Substitute x= 0 into the equation and solve for y.

3x+5y=30

Substitute

x= 0

3( 0)+5y=30

▼

Solve for y

ZeroPropMult

Zero Property of Multiplication

0+5y=30

IdPropAdd

Identity Property of Addition

5y = 30

DivEqn

.LHS /5.=.RHS /5.

y = 6

The y-intercept is (0,6). rc Equation: & 3x+5y = 30 x-intercept: & (10,0) y-intercept: & (0,6)

Plot the Intercepts

Now it is time to plot the intercepts in a coordinate plane.

Draw the Line Passing Through the Intercepts

Lastly, draw a line passing through these points.

Extra

General Formulas for the Intercepts of an Equation in Standard Form

Note that general formulas for the intercepts can be derived for any linear function written in standard form Ax+ By= C.

Assumption	x-intercept	y-intercept
A≠ 0, B≠ 0	(C/A,0)	(0,C/B)
A= 0, B≠ 0	The line is horizontal, y= C B, so it does not cross the x-axis.	(0,C/B)
A≠ 0, B= 0	(C/A,0)	The line is vertical, x= C A, so it does not cross the y-axis.

Exercises

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