Graphs with Intercepts

Find the \(X-\) and \(Y-\) Intercepts From the Equation of a Line

Use the equation of the line. To find:

• the \(x-\) intercept of the line, let \( y=0\) and solve for \( x\) .
• the \(y-\) intercept of the line, let \( x=0\) and solve for \( y\) .

Example 4.20

Find the intercepts of \(2x+y=6\).

Solution

We will let \(y=0\) to find the x- intercept, and let \(x=0\) to find the y- intercept. We will fill in the table, which reminds us of what we need to find.

To find the x-intercept, let \(y =0\)

	\(2 x+y=6\)
Let \(y=0\).	\(2 x+0=6\)
Simplify.	\(2 x=6\)
	\(x=3\)
The \(x\) -intercept is	\((3,0)\)
To find the \(y\) -intercept, let \(x=0\).
	\(2 x+y=6\)
Let \(x=0\).	\(2 \cdot 0+y=6\)
Simplify.	\(0+y=6\)
	\(y=6\)

The intercepts are the points (3,0) and (0,6) as shown in Table 4.26.

\(2x+y=6\)
\(x\)	\(y\)
3	0
0	6

Table 4.26

Try It 4.39

Find the intercepts of \( 3x+y=12\).

Try It 4.40

Find the intercepts of \( x+4y=8\).

Example 4.21

Find the intercepts of \(4x–3y=12\).

Solution

\(4 x=12\)

To find the \(x-\) intercept, let \(y = 0\).
	\(4 x-3 y=12\)
Let y = 0.	\(4 x-3 \cdot 0=12\)
Simplify.	\(4 x-0=12\)
	\(4x=12\)
	\(x=3\)
The \(x-\) intercept is	\((3, 0)\)
To find the y-intercept, let x = 0.
	\(4 x-3 y=12\)
Let \(x = 0\).	\(4 \cdot 0-3 y=12\)
Simplify.	\(0-3 y=12\)
	\(-3 y=12\)
	\(y=-4\)
The y-intercept is	\((0, −4)\)

The intercepts are the points \((3, 0)\) and \((0, −4)\) as shown in the following table.

4x−3y=12
x	y
3	0
0	−4

Try It 4.41

Find the intercepts of \( 3x–4y=12\).

Try It 4.42

Find the intercepts of \( 2x–4y=8\).