November 30

November 30

Word problems from 2 sets of points

Renting a gym

I rent a gym for $150.00 for 30 students, another time I rent the gym for $270.00 for 70 students. What is the fixed rate for renting the gym? What is the cost per student? What is the linear equation that will determine the price for any number of students?

Cost per student...?

It will cost $3 per student

Base fee for the gym...?

It costs $60 to rent the gym

 $y=3x+60$  

Median age of marriage

Couples are marrying later. The median age of men who tied the knot for the first time in 1970 was 23.2. In 1998, the median age was 26.7. What is the growth in age per year for first time marrying men? Write an equation, in slope intercept form to predict the median age that men marry for any year. What is the average age in 2020?

Growth per year in median marrying age...

0.125 age older per year

Linear model for median age at any year...

 $y=0.125x-223.05$  

Median age in 2020

29.45

Cost of owning a car

The number of dollars per month it costs you to own a car is a function of the number of kilometers per month you drive it. Based on information in an issue of Time magazine, the cost varies linearly with the distance, and is $366 per month for 300 miles per month, and $510 per month for 1500 miles per month. 

Cost per mile...

$0.12 per mile

Linear model for the cost of driving a car...

 $y=0.12x+330$  

Sketch a representation of what this problem will look like on a graph...

Which quadrants will you use to represent your graph? Why did you pick those quadrants?

Model of problem for graph

• My y-axis represents the cost because the cost is the dependent variable

• My x-axis represents my miles because mile is the independent variable

• Think...# of miles determine the cost

• I only used the 1st quadrant of the graph because in the real world there is no such thing as having negative miles driven every month.

Cost of 1,000 miles per month

$450

Cost of 2,000 miles per month

$570

How far could you drive without exceeding a monthly cost of $600

2,250 miles

Open Ended

What is the cost rate intercept? What does it tell you about the real world?

What is the cost rate intercept? What does it tell you about the real world?

• The cost rate intercept is another way of saying the y-intercept

• Our equation was

   $y=0.12x+330$  

• 330 is our y-intercept, or $330

• It represents the cost of driving a car even if you don't drive any miles; even if your car just sat in your driveway for the month you would still have to pay the monthly payments of owning a car.

Calculate the distance intercept.

-2,750

Open Ended

What does the distance intercept mean in the real world? Is it a valid real world representation?

What does the distance intercept mean in the real world? Is it a valid real world representation?

• The distance intercept is also known as the x-intercept.

• The x-intercept is negative, -2750

• This means that the car started costing you money 2,750 miles before you ever started driving it...negative distance is not applicable.