1. 1.4 Equations of Lines and Linear Models
Point-Slope Form
The line with slope m passing through the point (x1, y1)
has equation

2. 1.4 Examples Using Point-Slope
Example 1 Using the Point-Slope Form
Find the slope-intercept form of the line passing through the points shown. (1, 7) and (3, 3)
Solution

3. 1.4 Examples Using Point-Slope
Example 2 Using the Point-Slope Form
The table below shows a list of points found on the line Find the equation of the line.
Solution

4. 1.4 Standard Form of the Equation of a Line
A linear equation written in the form
where A, B, and C are real numbers, is said to be in
standard form.

5. 1.4 Equations of Lines in Ax + By = C Form
Graph
Analytic Solution
x-intercept: (2,0)
y-intercept: (0,3)
Graphing Calculator Solution

6. 1.4 Parallel Lines Parallel Lines
Two distinct nonvertical lines are parallel if and
only if they have the same slope.

7. 1.4 Parallel Lines Example Solution
Find the equation of the line that passes through the point (3,5) and is parallel to the line with equation Graph both lines in the standard viewing window.
Solution
Solve for y in terms of x.

8. 1.4 Parallel Lines 10
-10 10
-10

9. 1.4 Perpendicular Lines Perpendicular Lines
Two lines, neither of which is vertical, are
perpendicular if and only if their slopes have
product –1.

10. 1.4 Perpendicular Lines
Example Find the equation of the line that passes through the point
(3,5) and is perpendicular to the line with equation
Graph both lines in the standard viewing window.
Use slope from the previous example.
The slope of a perpendicular line is

11. 1.4 Perpendicular Lines 10
-15 15
-10

12. 1.4 Modeling Medicare Costs
Linear Models and Regression
Discrete data points can be plotted and the graph is called a scatter diagram.
Useful when analyzing trends in data.
e.g. Estimates for Medicare costs (in billions)
x (Year)
y (Cost)
2002
264
2003
281
2004
299
2005
318
2006
336
2007
354

13. 1.4 Modeling Medicare Costs
Scatter diagram where x = 0 corresponds to 2002, x = 1 to 2003, etc.
Data points (0, 264), (1, 281), (2, 299),
(3, 318), (4, 336) and (5, 354)
b) Linear model – pick 2 points,
(0, 264) and (3, 318)
c) Predict cost of Medicare in 2010.

14. 1.4 The Least-Squares Regression Line
Enter data into lists L1 (x list) and L2 (y list)
Least-squares regression line: LinReg in STAT/CALC menu

15. 1.4 Correlation Coefficient
Correlation Coefficient r
Determines if a linear model is appropriate
range of r:
r near +1, low x-values correspond to low y-values and high x-values correspond to high y-values.
r near –1, low x-values correspond to high y-values and high x-values correspond to low y-values.
means there is little or no correlation.
To calculate r using the TI-83, turn
Diagnostic On in the Catalog menu.

16. 1.4 Application of Least-Squares Regression
Example Predicting the Number of Airline Passengers
Airline Passengers (millions)
Airport
Harrisburg International
0.7
1.4
Dayton International
1.1
2.4
Austin Robert Mueller
2.2
4.7
Milwaukee General Mitchell
4.4
Sacramento Metropolitan
2.6
5.0
Fort Lauderdale-Hollywood
4.1
8.1
Washington Dulles
5.3
10.9
Greater Cincinnati
5.8
12.3

17. 1.4 Application of Least-Squares Regression
Scatter Diagram
Linear Regression:
Prediction for 2005 at Raleigh-Durham International using this model:
FAA’s prediction: 10.3 million 14 6 14 6