1. P.2 Linear Models and Rates of Change

2. Objectives Find the slope of a line passing through two points.
Write the equation of a line with a given point and slope.
Interpret slope as a ratio or as a rate in a real-life application.
Write equations of lines that are parallel or perpendicular to a given line.

3. Slope of a Line
slope
rise / run
∆y / ∆x
change in y / change in x

4. Slope
positive
negative
zero
no slope

5. Point-Slope Equation

6. Slope-Intercept Form

7. Example
Find the equation of a line that has slope 3 and passes through (1, -2).

8. Parallel and Perpendicular Lines
Two distinct non-vertical lines are parallel iff their slopes are equal.
Two distinct non-vertical lines are perpendicular iff m1=-1 / m2.

9. Example
Find the equation of a line that is parallel to 2x-3y=5 and passes through (2,-1).

10. Example
Find the equation of a line that is perpendicular to 2x-3y=5 and passes through (2,-1).

11. Technology Tip
Unless you have equal x and y scaling, graphs on the calculator many not appear to be perpendicular when they really are.
Try: y= 2/3 x – 5/3
Zoom 6
Zoom 5

12. P.4 Fitting Models to Data
Eruptions of Old Faithful

13. (Don't sketch graphs and don't use the standard form of a line.)
Homework
P.2: (p. 16)
#23-41 odd
61-67 odd
P.4: (p. 34) #1-4 all
(Don't sketch graphs and don't use the standard form of a line.)