1. Basic Algebra 2 Teacher – Mrs. Volynskaya
2.4 Using Linear Models
Basic Algebra 2
Teacher – Mrs. Volynskaya

2. The Trick: Converting Word Problems into Equations
Warm Up:
How many ways can a $50 bill be changed into $5 and $20 bills. Work with a partner and come up with as many combinations as possible.

3. How can we write this as an Algebraic Equation?
1st: Define your variables
Let’s let x = the number of $5 bills and y = the number of $20 bills
2nd: Set up an equation where the sum of the bills equals 50

4. We now have the equation 5x + 20y = 50
Next: Graph this equation. What do you notice?

5. What does it all mean?
Describe in your own words, what is going on in this graph?
Come up with as many different “revelations” as possible

6. More Examples
Suppose an airplane descends at a rate of 300 feet per minute from an elevation of 8000 feet. Write an equation to model the plane’s elevation as a function of the time it has been descending. Interpret the intercepts at which the graph intersects the vertical axis. Let d = distance and t = time.
Equation: d = -300t

7. Equation: d = -300t
Now, graph the equation. Why are the intercepts of the graph important?
8000 20 30

8. Making the best of data
Sometimes the points are not as nice as you like
A Trend Line is a line that approximates the relationship between the data points of a scatter plot. You can use it to make predictions by best fitting a line through the data.

9. Correlations positive
Outlier
As x increases
Then y increases
POSITIVE SLOPE
“Trend line”
or “regression line”

10. Correlations negative
As x increases
Then y decreases
Negative SLOPE

11. Correlations none
No real trend line