Holt CA Course 1

2-8 Graphing Equations

AF1.0 Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic expressions, solve simple linear equations, and graph and interpret their results.Also covered: NS2.3

California Standards

Holt CA Course 1

2-8 Graphing Equations

Vocabulary

linear equation

An equation whose solutions form a straight line on a coordinate plane.

Holt CA Course 1

2-8 Graphing EquationsExample 1: Finding Solutions of Equations with

Two Variables

Use the given x-values to write solutions of the equation as ordered pairs. y = 4x + 2; x = 1, 2, 3, 4.Make a table by using the given values for x to find values for y.

x 4x + 2 y

1 4(1) + 2 6

2 4(2) + 2 10

3 4(3) + 2 14

4 4(4) + 2 18

Write these solutions as ordered pairs.

(x, y)

(1, 6)

(2, 10)

(3, 14)

(4, 18)

Holt CA Course 1

2-8 Graphing Equations

Check if an ordered pair is a solution of an equation by putting the x and y values into the equation to see if they make it a true statement.

Holt CA Course 1

2-8 Graphing Equations

Example 2: Checking Solutions of Equations with Two Variables

Determine whether the ordered pair is a solution to the given equation.

(3, 21); y = 7x

y = 7x Write the equation.

21 = 7(3)?

21 = 21?

Substitute 3 for x and 21 for y.

So (3, 21) is a solution to y = 7x.

Holt CA Course 1

2-8 Graphing Equations

You can also graph the solutions of an equation on a coordinate plane. When you graph the ordered pairs given by some equations, they form a straight line. For this reason, these equations are called linear equations.

Holt CA Course 1

2-8 Graphing EquationsExample 3: Reading Solutions on Graphs

Use the graph of the linear equation to find the value of y for the given value of x.

x = 4

When x = 4, y = 2.

Start at the origin and move 4 units right.

Move up until you reach the graph. Move left to find the y-value on the y-axis.

The ordered pair is (4, 2).

x

y

-4 -2 0 2 4

4

-2

-4

2

Holt CA Course 1

2-8 Graphing Equations

Example 4: Graphing Linear Functions

Graph the equation y = –x – 2.

Make a table. Substitute different values for x.

x –x – 2 y

–1 –(–1) – 2 –1

0 –(0) – 2 –2

1 –(1) – 2 –3

Write the solutions as ordered pairs.

(x, y)

(–1, –1)

(0, –2)

(1, –3)

Holt CA Course 1

2-8 Graphing Equations

Example 4 Continued

x

y

Graph the ordered pairs on a coordinate plane.

-5 -4 -3 -2 -1 0 1 2 3 4 5

543

2

1

-5

-4-3-2

-1

Draw a line through the points to represent all the values of x you could have chosen and the corresponding values of y.

Holt CA Course 1

2-8 Graphing Equations Check It Out! Example 1

Use the given x-values to write solutions of the equation as ordered pairs. y = 3x + 2; x = 2, 3, 4, 5.

Make a function table by using the given values for x to find values for y.

x 3x + 2 y

2 3(2) + 2 8

3 3(3) + 2 11

4 3(4) + 2 14

5 3(5) + 2 17

Write these solutions as ordered pairs.

(x, y)

(2, 8)

(3, 11)

(4, 14)

(5, 17)

Holt CA Course 1

2-8 Graphing EquationsCheck It Out! Example 2

Determine whether the ordered pair is a solution to the given equation.

(4, 20); y = 5x

y = 5x Write the equation.

20 = 5(4)?

20 = 20?

Substitute 4 for x and 20 for y.

So, yes (4, 20) is a solution to y = 5x.

Holt CA Course 1

2-8 Graphing Equations Check It Out! Example 3

Use the graph of the linear function to find the value of y for the given value of x.

x = 2

When x = 2, y = 4.

Start at the origin and move 2 units right.

Move up until you reach the graph. Move left to find the y-value on the y-axis.

The ordered pair is (2, 4).

x

y

-4 -2 0 2 4

4

-2

-4

2

Holt CA Course 1

2-8 Graphing Equations

Check It Out! Example 4

Graph the equation. y = –x – 4

Make a table. Substitute different values for x.

x –x – 4 y

–1 –(–1) – 4 –3

0 –(0) – 4 –4

1 –(1) – 4 –5

Write the solutions as ordered pairs.

(x, y)

(–1, –3)

(0, –4)

(1, –5)

Holt CA Course 1

2-8 Graphing Equations

Check It Out! Example 4 Continued

x

y

Graph the ordered pairs on a coordinate plane.

-5 -4 -3 -2 -1 0 1 2 3 4 5

543

2

1

-5

-4-3-2

-1

Draw a line through the points to represent all the values of x you could have chosen and the corresponding values of y.