Holt Algebra 1

35 Using Intercepts

Warm Up 1. 5x + 0 = –10

Solve each equation.

–2

11

1

–2

2. 33 = 0 + 3y

3.

4. 2x + 14 = –3x + 4

5. –5y – 1 = 7y + 5

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* Find x- and y-intercepts and interpret their meanings in real-world situations.

* Use x- and y-intercepts to graph lines.

Learning Targets

Vocabulary

y-interceptx-intercept

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The y-intercept is the y-coordinate of the point where the graph intersects the y-axis. The x-coordinate of this point is always 0.

The x-intercept is the x-coordinate of the point where the graph intersects the x-axis. The y-coordinate of this point is always 0.

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Example 1: Finding Intercepts

Find the x- and y-intercepts.

The graph intersects the y-axis at (0, 1).

The y-intercept is 1.

The graph intersects the x-axis at (–2, 0).

The x-intercept is –2.

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Example 1: Finding Intercepts

5x – 2y = 10

5x – 2y = 10

5x – 2(0) = 10

5x – 0 = 10

5x = 10

To find the y-intercept, replace x with 0 and solve for y.

To find the x-intercept, replace y with 0 and solve for x.

x = 2The x-intercept is 2.

5x – 2y = 10

5(0) – 2y = 10

0 – 2y = 10 – 2y = 10

y = –5The y-intercept is –5.

Find the x- and y-intercepts.

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35 Using Intercepts

http://my.hrw.com/math11/math06_07/nsmedia/lesson_videos/alg1/player.html?contentSrc=6343/6343.xml

Holt Algebra 1

35 Using Intercepts

Example 1Find the x- and y-intercepts.4x + 2y = 16

4x + 2y = 16

4x + 2(0) = 16

4x + 0 = 16 4x = 16

To find the y-intercept, replace x with 0 and solve for y.

To find the x-intercept, replace y with 0 and solve for x.

x = 4The x-intercept is 4.

4x + 2y = 16

4(0) + 2y = 16

0 + 2y = 16 2y = 16

y = 8The y-intercept is 8.

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On Your Own! Example 1a

Find the x- and y-intercepts.

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On Your Own! Example 1bFind the x- and y-intercepts.–3x + 5y = 30

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http://my.hrw.com/math11/math06_07/nsmedia/lesson_videos/alg1/player.html?contentSrc=7503/7503.xml

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Example 2: Sports Application

Trish can run the 200 m dash in 25 s. The function f(x) = 200 – 8x gives the distance remaining to be run after x seconds. Graph this function and find the intercepts. What does each intercept represent?

Neither time nor distance can be negative, so choose several nonnegative values for x. Use the function to generate ordered pairs.

f(x) = 200 – 8x 200

250 5 10 20x

160 120 40 0

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Graph the ordered pairs. Connect the points with a line.

x-intercept: 25. This is the time it takes Trish to finish the race, or when the distance remaining is 0.

y-intercept: 200. This is the number of meters Trish has to run at the start of the race.

Example 2 Continued

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On Your Own! Example 2The school sells pens for $2.00 and notebooks for $3.00. The equation 2x + 3y = 60 describes the number of pens x and notebooks y that you can buy for $60.

Graph the function and find its intercepts.

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On Your Own! Example 2The school sells pens for $2.00 and notebooks for $3.00. The equation 2x + 3y = 60 describes the number of pens x and notebooks y that you can buy for $60.

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On Your Own! Example 2The school sells pens for $2.00 and notebooks for $3.00. The equation 2x + 3y = 60 describes the number of pens x and notebooks y that you can buy for $60.

What does each intercept represent?

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Example 3: Graphing Linear Equations by Using Intercepts

Use intercepts to graph the line described by the equation.3x – 7y = 21

Step 1 Find the intercepts.x-intercept: y-intercept:

3x – 7y = 21

3x – 7(0) = 21

3x = 21

x = 7

3x – 7y = 21

3(0) – 7y = 21

–7y = 21

y = –3

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Step 2 Graph the line.

Plot (7, 0) and (0, –3).

Connect with a straight line.

Example 3 Continued

Use intercepts to graph the line described by the equation.3x – 7y = 21

x

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Holt Algebra 1

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Example 3: Graphing Linear Equations by Using Intercepts

Use intercepts to graph the line described by the equation.y = –x + 4

Step 1 Write the equation in standard form.

y = –x + 4+x +x

x + y = 4

Add x to both sides.

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Example 3 Continued

Use intercepts to graph the line described by the equation.

Step 2 Find the intercepts.

x-intercept: y-intercept:

x + y = 4

x + 0 = 4

x = 4

x + y = 4

0 + y = 4

y = 4

x + y = 4

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Example 3 Continued

Use intercepts to graph the line described by the equation.

Step 3 Graph the line.

x + y = 4

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

Connect with a straight line.

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Use intercepts to graph the line described by the equation.

Step 1 Write the equation in standard form.

Example 3b

3y = x – 6

–x + 3y = –6

Multiply both sides 3, to clear the fraction.

Write the equation in standard form.

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Step 2 Find the intercepts.x-intercept: y-intercept:

–x + 3y = –6

–x + 3(0) = –6

–x = –6

x = 6

–x + 3y = –6

–(0) + 3y = –6

3y = –6

y = –2

Use intercepts to graph the line described by the equation.

Example 3b Continued

–x + 3y = –6

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Example 3b Continued

Step 3 Graph the line.

Plot (6, 0) and (0, –2).

Connect with a straight line.

Use intercepts to graph the line described by the equation.

–x + 3y = –6

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Use intercepts to graph the line described by the equation.

–3x + 4y = –12

Step 1 Find the intercepts.x-intercept: y-intercept:

On Your Own! Example 3a

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Use intercepts to graph the line described by the equation.

–3x + 4y = –12

On Your Own! Example 3

Step 2 Graph the line.