COMPARING EQUATIONS

Miss Jones rents a car for $50 a day andpays an administration fee of $100.

What is the equation of the line?

Do all the points on the table satisfy the equation y = 2x + 1? Explain your answer.

What is the slope of the line?

Write the equation of a line with a slope of -2 and the point (0, -3)

The cost to join a gym includes a one-time membership fee, plus a monthly fee.• Alice joined the gym and paid $250

for 6 months.• Peter joined and paid $400 for 9

months.

What is the monthly fee after the person joins the gym?

x y

0 1

1 3

2 5

Today we will use the four representations of equations to analyze and compare different linear situations.

You need to look at the graphs, tables, equations and situations.

You will be given enough information to answer the questions that follow.

Remember, you are COMPARING the situations. Look out for differences. How are the slopes different? How are the y-intercepts different?

The next slide will help you get started.

What to do…….

1.Read the entire question through.2.Look at any graphs, word problems or tables

that you have been given.

3.Because you are comparing two equations, write out at least two equations.

4.Answer the questions that are posed.

Look carefully at the problems on the next few slides.

Example one:

A zebra’s main predator is a lion. Lions can run at a speed of 53 feet per second over short distances. The graph below shows the speed of a zebra. Compare the speeds of the two animals.

Example two:The equation m = 140h, where m is the miles traveled in h hours, represents the speed of the first Japanese high speed train. The speed of a high speed train operating today in China is shown in the table. Assume the relationship between the two equations are linear.

a. Compare the equations’ y-intercepts and rates of change.

b. If you ride each train for 5 hours, how far will you travel on each?

Example three:

The number of new movies a store receives can be represented by the equation m = 7w + 2, where m represents the number of movies and w represents the number of weeks. The number of games the same store receives is shown in the table.

a.Compare the equations’ y-intercepts and rate of change.

b. How many new movies and games will the store have in 6 weeks?

Example four:

Angela and Benjamin each have a monthly cell phone bill. Angela’s monthly cell phone bill is represented by the equation y = 0.15x + 49, where x represents the minutes and y represents the cost. Benjamin’s monthly cost is shown in the graph.

Which of the two has the better deal? When will the bills be the same? What will the monthly bill be for 200 minutes?

Example five:

A museum charges $12.50 per adult ticket. The price of a student ticket is represented in the table.

Which statement is NOT true?a. The adult ticket price has a greater rate of change.b. Both equations have the same y-intercept.c. The student ticket price has a greater rate of change?d. Both equations go through the origin.

Example six:

Gabe gets a 1.5 mile head start and runs at a rate of 4.5 miles per hour. Taylor’s progress is represented by a graphthat goes through the points (1, 10), (2, 20), and (3,30). How long will Taylor need to run to catch up to Gabe?

CLASSWORK

Work in pairs to complete the worksheet COMPARING FUNCTIONS. You will have about 15 minutes.

After the 15 minutes are up, you and your partner will share your example and answers with the other partners in your group. You will have about 10 minutes to do this.

After your group has discussed the different scenarios, we will have a class discussion and record answers for your notes.

HOMEWORKComplete the worksheet Comparing Functions.

Show all your work. You will need to use loose leaf paper.

Look back at your notes if you need help.

Look at the next slide if you need internet help.

HOMEWORK HELP

https://www.youtube.com/watch?v=iCKX_LVVxB0

https://www.youtube.com/watch?v=Y7sccqRyATQ

https://www.youtube.com/watch?v=Pz5DfVrT_Fk