Warm Up Lesson Presentation Lesson Quiz - WordPress.com · 4.3 Lesson Quiz 2. A recycling company pays $1 per used ink jet cartridge and $2 per used laser cartridge. The company paid

4.3

Warm Up

Lesson Quiz

Lesson Presentation

Graph Using Intercepts

4.3 Warm-Up

Evaluate the expression when x = –3. 1. 3x + 4

ANSWER –5

2. –2x + 6

ANSWER 12

3. 4x – 3

ANSWER –15

4.3 Warm-Up

4. The amount a that a taxi service charges is given by a = 1.5m where m is the number of miles. Find a when m is 7.

ANSWER $10.50

4.3 Example 1

Substitute 0 for y.

Write original equation.

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

SOLUTION

Find the x-intercept and the y-intercept of the graph of 2x + 7y = 28.

Solve for x.

2x + 7(0) = 28

x = = 14 28 2

2x + 7y = 28

4.3 Example 1

2(0) + 7y = 28

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

Write original equation.

Substitute 0 for x.

Solve for y.

ANSWER

The x-intercept is 14. The y-intercept is 4.

2x +7y = 28

y = 28 7 = 4

4.3 Guided Practice

Find the x-intercept and the y-intercept of the graph of the equation. 1. 3x + 2y = 6

ANSWER 2, 3

2. 4x – 2y = 10

ANSWER 2.5, –5

3. –3x + 5y = –15

ANSWER 5, –3

4.3 Example 2

SOLUTION

STEP 1

Graph the equation x + 2y = 4.

x + 2y = 4

x = ← x-intercept 4

Find the intercepts.

x + 2(0) = 4 0 + 2y = 4

y = ← y-intercept 2

x + 2y = 4

4.3 Example 2

STEP 2

Plot points. The x-intercept is 4, so plot the point (4, 0). The y-intercept is 2, so plot the point (0, 2). Draw a line through the points.

4.3 Guided Practice

Graph the equation 6x + 7y = 42. Label the points where the line crosses the axes.

4.

ANSWER

4.3 Example 3

The graph crosses the x-axis at (2, 0). The x-intercept is 2. The graph crosses the y-axis at (0, –1). The y-intercept is –1.

Identify the x-intercept and the y-intercept of the graph shown at right.

ANSWER

4.3 Guided Practice

Identify the x-intercept and the y-intercept of the graph shown at the right.

5.

–4, 2 ANSWER

4.3 Example 4

EVENT PLANNING You are helping to plan an awards banquet for your school, and you need to rent tables to seat 180 people. Tables come in two sizes. Small tables seat 4 people, and large tables seat 6 people. This situation can be modeled by the equation

4x + 6y = 180

where x is the number of small tables and y is the number of large tables.

• Find the intercepts of the graph of the equation.

• Give four possibilities for the number of each size table you could rent.

• Graph the equation.

4.3 Example 4

SOLUTION

STEP 1 Find the intercepts.

4x + 6(0) = 180

x = ← x-intercept 45

4x + 6y = 180

4(0) + 6y = 180

y = ← y-intercept 30

4x + 6y = 180

4.3 Example 4

Since x and y both represent numbers of tables, neither x nor y can be negative. So, instead of drawing a line, draw the part of the line that is in Quadrant I.

Graph the equation.

The x-intercept is 45, so plot the point (45, 0).The y-intercept is 30, so plot the point (0, 30).

4.3 Example 4

STEP 3

Find the number of tables. For this problem, only whole-number values of x and y make sense. You can see that the line passes through the points (0, 30), (15, 20), (30, 10), and (45, 0).

So, four possible combinations of tables that will seat 180 people are: 0 small and 30 large, 15 small and 20 large, 30 small and 10 large,and 45 small and 0 large.

4.3 Guided Practice

6. WHAT IF? In Example 4, suppose the small tables cost $9 to rent and the large tables cost $14. Of the four possible combinations of tables given in the example, which rental is the least expensive? Explain.

45 small tables and no large tables; if you rent 45 small tables it costs $405, all other combinations are more expensive.

ANSWER

4.3 Example 5

SUBMERSIBLES A submersible designed to explore the ocean floor is at an elevation of –13,000 feet (13,000 feet below sea level). The submersible ascends to the surface at an average rate of 650 feet per minute. The elevation e (in feet) of the submersible is given by the function

e = 650t – 13,000 where t is the time (in minutes) since the submersible began to ascend.

4.3 Example 5

SOLUTION

STEP 1

13,000 = 650t

650t – 13,000 0 =

Find the intercepts.

= t 20 ← t-intercept

= –13,000 e ← e-intercept

e = 650(0) – 13,000

• Graph the function and identify its domain and range.

• Find the intercepts of the graph of the function and state what the intercepts represent.

4.3 Example 5

The t-intercept represents the number of minutes the submersible takes to reach an elevation of 0 feet (sea level). The e-intercept represents the elevation of the submersible after 0 minutes (the time the ascent begins).

4.3 Example 5

Graph the function using the intercepts.

The submersible starts at an elevation of –13,000 feet and ascends to an elevation of 0 feet. So, the range of the function is –13,000 ≤ e ≤ 0. From the graph, you can see that the domain of the function is 0 ≤ t ≤ 20.

STEP 2

4.3 Guided Practice

WHAT IF? In Example 5, suppose the elevation of a second submersible is given by e = 500t – 10,000. Graph the function and identify its domain and range.

7.

domain: 0 ≤ t ≤ 20, range: –10,000 ≤ e ≤ 0

ANSWER

4.3 Lesson Quiz

1. Find the x-intercept and the y-intercept of the graph of 3x – y = 3.

x-int: 1, y-int: –3 ANSWER

4.3 Lesson Quiz

2. A recycling company pays $1 per used ink jet cartridge and $2 per used laser cartridge. The company paid a customer $14. This situation is given by x + 2y = 14 where x is the number of ink jet cartridges and y the number of laser cartridges. Use intercepts to graph the equation. Give four possibilities for the number of each type of cartridge that could have been recycled.

ANSWER (0, 7), (6, 4), (10, 2), (14, 0)