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### 4.4 Graphing Lines Using Intercepts

WARM UP

5 Minutes Remain

Evaluate the expression.

17 – 6 + 4 – 8

6 + 9 ÷ 3 + 3

4 • 5 – 2 • 6

9 • 6 ÷ 3 • 18

22 – 8 ÷ 2 • 3

WARM UP

4

Evaluate the expression.

17 – 6 + 4 – 8

6 + 9 ÷ 3 + 3

4 • 5 – 2 • 6

9 • 6 ÷ 3 • 18

22 – 8 ÷ 2 • 3

WARM UP

3

Evaluate the expression.

17 – 6 + 4 – 8

6 + 9 ÷ 3 + 3

4 • 5 – 2 • 6

9 • 6 ÷ 3 • 18

22 – 8 ÷ 2 • 3

WARM UP

2

Evaluate the expression.

17 – 6 + 4 – 8

6 + 9 ÷ 3 + 3

4 • 5 – 2 • 6

9 • 6 ÷ 3 • 18

22 – 8 ÷ 2 • 3

WARM UP

1

Evaluate the expression.

17 – 6 + 4 – 8

6 + 9 ÷ 3 + 3

4 • 5 – 2 • 6

9 • 6 ÷ 3 • 18

22 – 8 ÷ 2 • 3

WARM UP

0

Evaluate the expression.

17 – 6 + 4 – 8

6 + 9 ÷ 3 + 3

4 • 5 – 2 • 6

9 • 6 ÷ 3 • 18

22 – 8 ÷ 2 • 3

Today’s Schedule:

Lesson 4.4 Powerpoint

In class assignment/homework

Exit Slip

GOAL: Find the intercepts of the graph of a linear equation and then use them to make a quick graph of the equation.

KEY WORDS: x-intercepts, y-intercepts, x-axis, y-axis.

4.4 Graphing Lines Using Intercepts

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

A y-intercept is the y-coordinate of a point where a graph crosses the y-axis

The y-intercept is the value of y when x = 0. Here, the y-intercept is 2.

The x-intercept is the value of x when y = 0. Here, the x-intercept is 3.

4.4 Graphing Lines Using Intercepts

EXAMPLE 1 Find an x-intercept

Find the x-intercept of the graph of the equation 2x + 3y =6

SOLUTION

To find an x-intercept, substitute 0 for y and solve for x.

STEP ONE: Write the original equation 2x + 3y = 6

STEP TWO: Substitute 0 for y 2x + 3(0) = 6

STEP THREE: Solve for x x = 3

ANSWER> The x-intercept is 3. The line crosses the x-axis at the point (3,0)

4.4 Graphing Lines Using Intercepts

EXAMPLE 2 Find a y-intercept

Find the y-intercept of the graph of the equation 2x + 3y =6

SOLUTION

To find a y-intercept, substitute 0 for x and solve for y.

STEP ONE: Write the original equation 2x + 3y = 6

STEP TWO: Substitute 0 for x 2(0) + 3y = 6

STEP THREE: Solve for y y = 2

ANSWER> The y-intercept is 2. The line crosses the y-axis at the point (0,2)

4.3 Horizontal and Vertical Lines

CHECK POINT Find Intercepts

Find the x-intercept of the graph of the equation 3x – 4y = 12

Find the y-intercept of the graph of the equation 3x – 4y = 12

4.4 Graphing Lines Using Intercepts

SUMMARY

Making a Quick Graph

STEP ONE Find the intercepts.

STEP TWO Draw a coordinate plane that includes the intercepts.

STEP THREE Plot the intercepts and draw a line through them.

4.4 Graphing Lines Using Intercepts

EXAMPLE 3 Make a Quick Graph

Graph the equation 3x + 2y = 12

SOLUTION

Find the intercepts.

STEP ONE: Write the original equation

3x + 2y = 12

STEP TWO: Substitute 0 for y

3x + 2(0) = 12

STEP THREE: Solve for x

x = 4

1

4.4 Graphing Lines Using Intercepts

EXAMPLE 3 Make a Quick Graph

Graph the equation 3x + 2y = 12

SOLUTION

Find the intercepts.

STEP ONE: Write the original equation

3x + 2y = 12

STEP TWO: Substitute 0 for x

3(0) + 2y = 12

STEP THREE: Solve for y

y = 6

1

4.4 Graphing Lines Using Intercepts

EXAMPLE 3 Make a Quick Graph

Graph the equation 3x + 2y = 12

SOLUTION

Draw a coordinate plane that includes the points (4,0) and (0,6).

2

4.4 Graphing Lines Using Intercepts

EXAMPLE 3 Make a Quick Graph

Graph the equation 3x + 2y = 12

SOLUTION

Plot the points (4,0) and (0,6) and draw a line through them.

3

4.4 Graphing Lines Using Intercepts

CHECK POINT Make a Quick Graph

Graph the equation using intercepts.

2x + 5y = 10

x – 6y = 6

4x -5y = 20

YOU’RE CERTIFIED

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