Rates of Change Slope

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
rise
change in y


run
change in x
Also,
m

where
A line has the same slope everywhere.
In your text, read about slope on page 10.
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).

Lets see if we have enough information to write
an equation
Do we have the slope?
Since we have the slope and a point, we can then
use the point-slope formula for a line.
Do we have a point?
Ans
I prefer writing the equation of a line in
slope-intercept form(y mx b form), but your
text will sometimes give you the general equation
of the line. With just a bit of algebra, you can
check your result.
7
Examples of Horizontal and Vertical Lines
Example Find an equation of a vertical line
that passes through the point (-2, 6).
This example is rather simple. We dont need the
slope to write this equation since we know all
the points on a vertical line share the same
x-coordinatethus the equation of the vertical
line in this case is
Example Find an equation of a horizontal line
that passes through the point (-2, 6).
The slope of a horizontal line is 0. Since all
the points on a horizontal line share the same
y-coordinate, the equation can be written as
8
Graphing Lines Using Slope-Intercept Method
Example Sketch the graph of
using the slope-intercept method.
m 2
In this case,
b 1
m slope b y-intercept
y
to the right 1
Graph the y-intercept and then count the slope.
Remember, slope is rise over run.
up 2
x
9
More Examples of Lines
Ex Sketch the graph of
Ex Sketch the graph of
This will be a vertical line with an x-intercept
of -2.
This will be a horizontal line with a y-intercept
of 3.
Note This is not a function
y
y
x
x
zero
undefined
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 equal.

• Two distinct nonvertical lines are perpendicular
  iff their slopes are negative reciprocals 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).
We need the slope and a point. The slope we need
will be the same as the slope for the equation
given since parallel lines have the same slope.
To find the slope, write x y 7 in
slope-intercept form to read the m value.
Now, use the slope and the point to write the
equation using the point-slope form of a line.
Again, I like to write my final answer in
slope-intercept form instead of the general form.
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).
We need the slope and a point. The slope we need
will be the negative reciprocal of the slope we
find from the equation given since perpendicular
lines have negative reciprocal slopes.
To find the slope, write x y 7 in
slope-intercept form to read the m value.
Use the negative reciprocal which is 1.
Now, use the slope (1) and the point, (-3, 2), to
write the equation using the point-slope form of
a line.
On page 15 of your text, read the Technology
Pitfall
14
Homework
Section P.2 pages 16- 17 1-5 odd, 15-19 odd,
23-29 odd, 35, 37, 39, 43, 57-61 odd, 69, 71