GRAPHING LINEAR EQUATIONS USING INTERCEPTS

The following steps will be useful to graph a linear equation using intercepts.

Step 1 :

Find the x-intercept by letting y = 0 and solving for x. Use the x-intercept to plot the point where the line crosses the x-axis.

Step 2 :

Find the y-intercept by letting x = 0 and solving for y. Use the y-intercept to plot the point where the line crosses the y-axis.

Step 3 :

Draw a line through the two points.

Use intercepts to graph the line described by each equation.

Example 1 :

2x + 3y = 12

Solution :

Find the intercepts.

x-intercept :

2x + 3y = 12

2x + 3(0) = 12

2x + 0 = 12

2x = 12

2x/2 = 12/2

x = 6

(6, 0)

y-intercept :

2x + 3y = 12

2(0) + 3y = 12

0 + 3y = 12

3y = 12

3y/3 = 12/3

y = 4

(0, 4)

Plot (6, 0) and (0, 4).

Connect with a straight line.

Example 2 :

-2x + 8y = 16

Solution :

Find the intercepts.

x-intercept :

-2x + 8y = 16

-2x + 8(0) = 16

-2x + 0 = 16

-2x = 16

-2x/(-2) = 16/(-2)

x = -8

(-8, 0)

y-intercept :

-2x + 8y = 16

-2(0) + 8y = 16

0 + 8y = 16

8y = 16

8y/8 = 16/8

y = 2

(0, 2)

Plot (-8, 0) and (0, 2).

Connect with a straight line.

Example 3 :

y = -0.5x - 1.5

Solution :

Find the intercepts.

x-intercept :

y = -0.5x - 1.5

0 = -0.5x - 1.5

0.5x = -1.5

x = -3

(-3, 0)

y-intercept :

y = -0.5x - 1.5

y = -0.5(0) - 1.5

y = 0 - 1.5

y = -1.5

(0, -1.5)

Plot (-3, 0) and (0, -1.5).

Connect with a straight line.

Example 4 :

y = 2x/3 + 4

Solution :

Find the intercepts.

x-intercept :

y = 2x/3 + 4

0 = 2x/3 + 4

-4 = 2x/3

-12 = 2x

-6 = x

(-6, 0)

y-intercept :

y = 2x/3 + 4

y = 2(0)/3 + 4

y = 0/3 + 4

y = 0 + 4

y = 4

(0, 4)

Plot (-6, 0) and (0, 4).

Connect with a straight line.

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GRAPHING LINEAR EQUATIONS USING INTERCEPTS

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