examples and guided practice come from the algebra 1 powerpoint presentations available at

Examples and Guided Practice come from the Algebra 1 PowerPoint Presentations

available at www.classzone.com

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.

Find the intercepts of the graph of an equationEXAMPLE 1

Solve for x.

2x + 7(0) = 28

x = = 14282

2x + 7y = 28

2(0) + 7y = 28

Find the intercepts of the graph of an equation

EXAMPLE 1

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 = 287 = 4

Find the x-intercept and the y-intercept of the graph of the equation.

GUIDED PRACTICE for Example 1

1. 3x + 2y = 6

ANSWER 2, 3


2. 4x – 2y = 10


ANSWER 2.5, –5


3. –3x + 5y = –15


ANSWER 5, –3

SOLUTION

STEP 1

Use intercepts to graph an equationEXAMPLE 2

Graph the equation x + 2y = 4.

x + 2y = 4

x = x-intercept4

Find the intercepts.

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

y = y-intercept2

x + 2y = 4

Use intercepts to graph an equationEXAMPLE 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.

Use a graph to find interceptsEXAMPLE 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.

Use intercepts to graph an equationEXAMPLE 2GUIDED PRACTICE for Examples 2 and 3

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

4.

ANSWER

GUIDED PRACTICE for Examples 2 and 3

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

5.

–4, 2ANSWER

EVENT PLANNING

Solve a multi-step problemEXAMPLE 4

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.

SOLUTION

STEP 1


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

• Graph the equation.


4x + 6(0) = 180

x = x-intercept45

4x + 6y = 180

4(0) + 6y = 180

y = y-intercept30

4x + 6y = 180


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.

STEP 2

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).


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.

GUIDED PRACTICEEXAMPLE 2GUIDED PRACTICE for Example 4

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

SUBMERSIBLES

Use a linear modelEXAMPLE 5

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.

SOLUTION

Use a linear modelEXAMPLE 5

STEP 1

13,000 = 650t

650t – 13,0000 =


= t20 t-intercept

= –13,000e e-intercept

e = 650(0) – 13,000

• Graph the function and identify its domain and range.

• Find the intercepts of the graph of the functionand state what the intercepts represent.

Use a linear model

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).

Use a linear model

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

Use a linear model

EXAMPLE 5GUIDED PRACTICE for Example 5

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

examples and guided practice come from the algebra 1 powerpoint presentations available at

Documents