x

y

1. Which of the following is the equation of the line shown?

3x32y

2x32y

3x23y

2x23y

3x23y

a.

b.

c.

d.

e.

3. Write the equation of the line which passes through the points (3, 10) and (–1, 2).

Exit Ticket

2. Write the equation of the line with slope and that passes through

the point (8, –3).

2

1

72

1 xy

4x2y

Answers to even-numbered HW problems

Section 3.2

S-2 The slope is – . S-8 f(x) = – 3x + 14 or y = – 3x + 14

Ex 8a) N = .03T – 9256

b) Slope is .03, vertical intercept is -9256

c) The fixed monthly costs are $9,256.

d) The agency charges 3% commission.

e) The horizontal intercept is 308,533. It represents the amount in total sales for the agency to break even.

45

The next screen you see may SCARE some of you.

From IRS Instructions for completing the 1040 individual tax form for 2013

From IRS Instructions for completing the 1040 individual tax form for 2013

I = Income 33,000 33,200 33,400 33,600 33,800

T = Tax 4,508 4,538 4,568 4,598 4,628

Set up for graphs of data

Setting the viewing window

Entering data into lists

I = Income 33,000 33,200 33,400 33,600 33,800

T = Tax 4,508 4,538 4,568 4,598 4,628

I = Income 33,000 33,200 33,400 33,600 33,800

T = Tax 4,508 4,538 4,568 4,598 4,628

Since the graph of this data appears to be linear, there

should be a linear function that passes through the

data points.

We say that the data can be modeled by a

linear function.

I = Income 33,000 33,200 33,400 33,600 33,800

T = Tax 4,508 4,538 4,568 4,598 4,628

200 200 200 200

30 30 30 30

Change in I 200 (33,000 to 33,200)

200 (33,200 to 33,400)

200 (33,400 to 33,600)

200 (33,600 to 33,800)

Change in T 30 30 30 30

Table of Differences

I = Income 33,000 33,200 33,400 33,600 33,800

T = Tax 4,508 4,538 4,568 4,598 4,628

200 200 200 200

30 30 30 30

What is the slope of the linear function for Tax in terms of Income?

What is the formula (equation) for the linear function?

When data are linear:

A data table with evenly spaced values for x can be modeled with a linear function if it shows a constant change in y.

If the x-values are evenly spaced but the change in y is not constant, then the data cannot be modeled exactly by a linear function.

15.200

30m

44215 xy IT

I = Income 33,000 33,200 33,400 33,600 33,800

T = Tax 4,508 4,538 4,568 4,598 4,628

I = Income 48,000

48,600 51,000

54,400

T = Tax 7,935 8,085 8,685 9,535

When data are linear:

A data table with unevenly spaced values for x can be modeled with a linear function if the slope between all pairs of consecutive data points is the same.

Can this data still be modeled with a linear function?

600 2400

150 600 850

3400

25.3400

850

2400

600

600

150

I = Income 48,000

48,600 51,000

54,400

T = Tax 7,935 8,085 8,685 9,535

What is the equation for the linear function that models this data? Graph the data and the linear model on your calculator.

4065.25IT

When data are linear:

A data table with unevenly spaced values for x can be modeled with a linear function if the slope between all pairs of consecutive data points is the same.

Can this data still be modeled with a linear function?

600 2400

150 600 850

3400

25.3400

850

2400

600

600

150

I = Income 48,000

48,600 51,000

54,400

T = Tax 7,935 8,085 8,685 9,535

What is the equation for the linear function that models this data? Graph the data and the linear model on your calculator.

4065.25IT

55,300

9,760

I = Income 48,000

48,600 51,000

54,400

T = Tax 7,935 8,085 8,685 9,535

55,300

9,760

Homework:

Read Section 3.3 (through bottom of page 252)

Page 258 # S-1, S-2, S-3, S-17, S-18

Pages 259–263 # 1, 2, 3, 12

I was on the second day of a road trip when I decided to keep a record of how far I had traveled from home. The table below shows how many hours I drove that day and how far I was away from home. For example, after I had traveled a total of 3½ hours, I was 366 miles away from home.

Number of hours traveled

on day 2

Distance from home (in miles)

2 282

3½ 366

6 506

8 618

8½ 646

Without graphing, determine if the data in the table below are linear.

Exit Ticket

a. Find the linear model (equation) for the data.

b. Graph the data points and the model on your calculator. Call your teacher over to see your calculator screen.

c. How far was I from home at the start of the day?