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In this lesson, you will learn to use intercepts to graph a line. Recall that a y-intercept is the y-coordinate of a

point where a graph crosses the y-axis. The x-intercept is the x-coordinate of a point where a graph crosses

the x-axis.

One form of a linear equation, called standard form, allows you to find intercepts quickly. You can use the

intercepts to then draw the graph.

KEY CONCEPT: STANDARD FORM OF A LINEAR EQUATION

The standard form of a linear equation, where A, B, and C are real numbers, and A and B are not both zero is

!" # $% & '

PROBLEM 1: FINDING X- AND Y-INTERCPETS

Find the x- and y-intercepts of the graph of each equation.

1.

(" # )% & *)

2.

+" , -% & -.

3.

(" # /% & ,0*

4.

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5.

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6.

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7.

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8.

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Vocabulary

Review

p

z

Chapter 5 154

5-5

Standard Form

Underline the correct word to complete each sentence.

1. Line z is a horizontal / vertical line.

2. Line p is a horizontal / vertical line.

3. A line with a slope of 0 is horizontal / vertical .

4. A line with an undefined slope is horizontal / vertical .

Vocabulary Builder

standard (adjective) STAN durd

Other Word Forms: standards (plural noun), standardized (adjective)

Main Idea: Something that is standard is well known and widely used.

Example: The standard measure of weight used in the U.S. is the pound.

Math Usage: The standard form of a linear equation is Ax 1 By 5 C, where A, B,

and C are real numbers, and A and B are not both zero.

Opposites: different, irregular

Use Your Vocabulary

Underline the correct word(s) to complete each sentence.

5. In gymnastics, judges use a set of standards / standardized to award a score.

6. Most English words have a standard / standardized pronunciation.

7. Many states use standard / standardized tests to assess their students’ performance.

8.

Multiple Choice Which linear equation is in standard form?

y 526x 1 4 3x 2 7y 5 42

y 527x 2 3 y 2 6 5 2(x 1 7)

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PROBLEM 2: GRAPHING A LINE USING INTERCEPTS

Graph each equation using the x- and y-intercepts.

9.

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10.

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11.

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12.

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13.

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14.

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PROBLEM 3: GRAPHING HORIZONTAL AND VERTICAL LINES

If

! & .

in the standard form

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, then you can write the equation in the form

% & 2

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2

is a

constant. If

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3

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% & 2

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is a vertical line.

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16.

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17.

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18.

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PROBLEM 4: TRANSFORMIING TO STANDARD FORM

Given an equation in slope-intercept form or point-slope form, you can rewrite the equation in standard form

using only integers.

Write eqch equation in standard form using integers.

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PROBLEM 5: USING STANDARD FORM AS A MODEL

27. A media download store sells songs for $2 each and movies for $12 each. You have $60 to spend. Write

and graph an equation that describes the items you can purchase. What are three combinations of numbers

of songs and movies you can purchase?

28. In a video game, you earn 5 points for each jewel you find. You earn 2 points for each star you find. Write

and graph an equation that represents the numbers of jewels and stars you must find to earn 250 points.

What are three combinations of jewels and stars you can find that will earn you 250 points?

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29. A store sells T-shirts for $12 each and sweatshirts for $15 each. You plan to spend $120 on T-shirts and

sweatshirts. Write and graph an equation that represents this situation. What are three combinations of T-

shirts and sweatshirts you can buy for $120?

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3x − y = 9

4x +12 y = −18

7x − 2 y = 4

−3x + y = 6

−2x − 4 y = 8

2 − y = x − 6

x = 4

y = −2

y = 4 x − 7

y = −

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y =

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8x −10y = −100

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