2.1: Linear Expressions and Equations

Warm-up:

 

 

1. Write a formula for the linear equation that satisfies the following properties:

1. \(f(2)=3\) and \(f\) has slope of -4.
   
   
   
    
2. \(g\) has slope 2 and passes the y -axis at  \(g(t)=13\).
   
   
   
    
3. \(f\) passes through the points \((-4,5)\) and \((8,10)\)
   
   
   
    
4. \(h(-4)=5\) and \(h(8)=10\)
   
   
   
    
5. \(f(-6)=7\) and \(f(3)=-6\)
   
   
   
    
6. \(d\) passes through the points (-18, -290) and \((20,312)\)
   
   
   
    

2. Use the following table to answer the questions below.

Year t	0	1	2
Value of the company \(V=f(t)\)	2000	1500	1000

 

1. What does this table represent in practical terms?
   
   
   
    
2. Write a formula for f(t).
   
   
   
    
3. Use your formula to find when the value of the computer is \$250.
   
   
   
    

3. The solid waste generated each year in the cities of the US is increasing. The solid waste generated, in millions of tons, was 88.1 in 1960 and 249.9 in 2010. The trend appears linear during this time.

1. Construct a formula for the amount of municipal solid waste generated in the US by finding the equation of the line through these two points.
   
   
   
    
2. Use this formula to predict the amount of municipal solid waste generated in the US, in millions of tons, in the year 2020.
   
   
   
    
3. Your formula might seem a little weird. What is the "initial amount" of this formula? To fix this, create a new formula that describes the amount of municipal solid waste generated since 1980. (In other words, treat the year 1980 as \(t=0\).) Then, verify that your formula is also correct by finding the waste generated in 2020.
    

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