Application of Linear Equation Example 1 WEEK 10 LESSON 3: PRESS SPACE BAR TO NAVIGATE THROUGH SLIDESHOW.

Application of Linear Equation Example 1WEEK 10 LESSON 3: PRESS SPACE BAR TO NAVIGATE THROUGH SLIDESHOW.

What we Have LearnedSO FAR WE HAVE LEARNED HOW TO FIND EQUATIONS OF LINES GIVEN:

1.) TWO POINTS

2.) THE SLOPE AND Y-INTERCEPT

3.) A GRAPH

4.) A TABLE OF DATA

NOWWE WILL USE THESE SKILLS TO SOLVE LINEAR APPLICATION

PROBLEMS.

In the year 1995, approximately 87 million people in America were fans of American football.  In the year 2014, there were approximately 187 million people who were fans of football.  The NFL needs to decide when to add an expansion team to the league.  To do so, there must be 300 million fans of American football.  (Assume the increase in fans per year is approximately linear).

Identify the important information.

a.)”In the year 1995, approximately 87 million”

b.)“In the year 2014, there were approximately 187 million”c.) there must be 300 million fans of American football (to add expansion team.

d.)“increase in fans per year is approximately linear”

Questions to Answer

1.) How fast is the number of fans changing each year?

2.) By what year would the NFL consider adding an expansion team?

What does each piece of information mean?

”In the year 1995, approximately 87 million”This is giving us one coordinate point. 1995 is the starting year (x) which equals time 0 and there are 87 million fans (y). The coordinate is (0,87)Note: We will add millions at the end for units so we don’t have to work with tons of zeros!

“In the year 2014, there were approximately 187 million”We have a second point here. To find ‘x’ we ask how many years have passed between 1995 and 2014. (2014-1995 = 19) 187 is our ‘y’. The coordinate point is (19, 187)

There must be 300 million fans of American football (to add expansion team.)

The number of fans is our y-variable so we have a third ‘y’ value but no value of ‘x’ (the year there are 300 million fans)

Increase in fans per year is approximately linear.

This gives us that the relationship between the number of fans and the year is linear. So we know we can use the equation y = mx+b. To use it we must find the slope (m) and y-intercept (b).

In the year 1995, approximately 87 million people in America were fans of American football.  In the year 2014, there were approximately 187 million people who were fans of football.  The NFL needs to decide when to add an expansion team to the league.  To do so, there must be 300 million fans of American football.  (Assume the increase in fans per year is approximately linear).

Use the two points (Coordinates) you found in the previous step.

(0,87) (19, 187)

With two points you can now find the slope.

187- 87 = 100 19- 0 = 19

Now you need the y-intercept. Remember that any point where x = 0 gives you the y-intercept (b).

b = 87

Input the information you have in the equation

Now you have enough information to solve the problem!

In the year 1995, approximately 87 million people in America were fans of American football.  In the year 2014, there were approximately 187 million people who were fans of football.  The NFL needs to decide when to add an expansion team to the league.  To do so, there must be 300 million fans of American football.  (Assume the increase in fans per year is approximately linear).

How fast are the number of fans changing each year?

Any question about how fast or slow (the rate) something is changing you are being asked for the slope. In this case we found that the slope = .

The meaning of the slope is that the number of fans is increasing by 100 million fans every 19 years.

You can calculate to a decimal as well and get an increase of 5.26 millions fans per year. The reason is per year is any number without a visible denominator is 1 so the slope is 5.26/1.

By what year would the NFL consider adding an expansion team?

In this Question you are being asked about ‘what year’ or ‘when’

(your ‘x’ value) something is going to happen.

In order for the NFL to add an expansion team there needs to be 300 million fans.

Therefore you are given ‘y’ and you are solving for ‘x’. Input 300 into the equation we found previously (

The new equation will look like this. (or you can use 100/19 for the slope if you prefer.)

Solve for ‘x’ by isolating and you get approximately 40 years. To find the actual year it is the starting , 1995 + 40 = 2035

In the year 1995, approximately 87 million people in America were fans of American football.  In the year 2014, there were approximately 187 million people who were fans of football.  The NFL needs to decide when to add an expansion team to the league.  To do so, there must be 300 million fans of American football.  (Assume the increase in fans per year is approximately linear).

Return to the Class Site to view Videos of creating

equations from word problems.