1. Section 1.3 Modeling with Linear Functions
Honors Algebra 2
Section 1.3
Modeling with Linear Functions

2. What are some “real life” examples where something increases or decreases over time?

3. Essential question
How can I write an equation of a line when given information about the line?

4. Writing a linear equation from a graph
#1 Observe the slope and the y-intercept and plug them into 𝑦=𝑚𝑥+𝑏

5. Caution!
Don’t just count spaces for slope if the increments are different!

6. Writing a linear equation given a point and the slope or two points
Use point-slope form 𝑦− 𝑦 1 =𝑚(𝑥− 𝑥 1 ). Plug in the slope and any point on the line.
Solve for y and you have slope-intercept form!

7. Numbers are not always “nice.”

8. You can make a scatter plot of your data
You can make a scatter plot of your data. Frequently “real data” has points that do not all lie on a line.

9. Essential question?
How can I make a line that fits a scatter plot of my data?

10. You can straddle all the points and draw a line
You can straddle all the points and draw a line. You should have about the same number of points above and below the line.

11. When you have drawn a line on the scatter plot, you can find the equation of that line.

12. The equation models the data.
Everyone’s equations will vary. (Remember we approximated the middle of the points)

13. When the points in a scatter plot are close to a line, it is easy to get a good line of best fit.

14. A correlation coefficient (r) is a number,
from -1 to 1, that measures how well a line fits a set of data pairs.

15. Lines of best fit with a positive slope will have an r value from 0 to 1.
Lines of best fit with a negative slope will have an r value from -1 to 0.

16. Using a calculator to find the line of best fit.
Press STAT then Edit to get to the lists
To clear data already in the list, arrow to the top and press CLEAR. NEVER press DEL!!!!!!!
Enter data
Press STAT, arrow to CALC, then press 4 (LinReg), then ENTER.
The calculator will display the slope and y-intercept of the line and the r value.

17. Assignment #3
Pg. 26 #1-8 all, 9-31 odd