1. Rates of Change (Slope)
Section P.2

2. After this lesson, you should be able to:
find the slope of a line passing through two points
write the equation of a line given the point and the slope
sketch the graph of a linear equation in slope-intercept form
write equations of lines that are parallel or perpendicular to a given line

3. Slope of a Line m = = = change in y change in x rise run Slope: Also,
where
A line has the same slope everywhere.

4. Equations of Lines To write the equation of a line, you need:
one point
the slope
Remember: Equations of lines are first degree equations.

5. Point-Slope Equation of a Line
Given the slope m passing through the point ,
an equation of the line can be written in the form

6. Example
Example: Find an equation of a line that has a slope of 4 and passes through the point (-2, 3).

7. Examples of Horizontal and Vertical Lines
Example: Find an equation of a vertical line that passes through the point (-2, 6).
Example: Find an equation of a horizontal line that passes through the point (-2, 6).

8. Graphing Lines Using Slope-Intercept Method
Example: Sketch the graph of using the slope-intercept method.
m = 2
b = 1
In this case,
up 2
to the right 1
m = slope
b = y-intercept x y

9. More Examples of Lines Ex: Sketch the graph of Ex: Sketch the graph of
This will be a _______________ line with a __-intercept of 3.
This will be a ____________ line with an ____-intercept of -2. x y x y
Note: This is not a function
What is the slope of the line?
What is the slope of the line?

10. Summary of Lines General form: Ax + By + C = 0 Vertical line: x = a
Horizontal line: y = b
Point-slope form: y – y1 = m(x –x1)
Slope-intercept form: y = mx + b

11. Parallel and Perpendicular Lines
Two distinct nonvertical lines are parallel iff their slopes are____________________.
Two distinct nonvertical lines are perpendicular iff their slopes are _______________ _________________ of each other.

12. Example-Parallel Line
Example: Write an equation of the line that is parallel to the line x + y = 7 and passes through the point (-3, 2).

13. Example-Perpendicular Line
Example: Write an equation of the line that is perpendicular to the line x + y = 7 and passes through the point (-3, 2).

14. Another Example— Parallel and Perpendicular Lines
Find the general form equation of the line that passes through and is
a) parallel to b) perpendicular to

15. MAT SPRING 2007
Homework
Section P.2: pages #1-5 odd, odd, odd, 35, 37, 39, 43, odd, 69, 71