Chapter 4 Note Guide
Name: _________________
Section 4 – 1: Slope
Which line is steeper?
Slope:
1) The ratio of the change in the y-coordinates (_________) to the change in the xcoordinates (________).
2) Notated with the letter m.
3) Slope is: m 
Rise
Run
Examples:

State the slope
of the following line.
1).
2).
3).
4).
Finding the Slope of Two Points.
The slope m of a nonvertical line through any points (x1, y1) and (x2, y2 ) can be found
y y
as follows m  2 1
x 2  x1
Example: State the Slope of the line



1) The line that goes through (-3, 2) and (5, 4).
2) The line that goes through (-3, 4) and (4,4).
3) The line that goes through (-3, 4) and (-2, 8).
4) The line that goes through (-2, -4) and (-2, 3).
Concept Summary: Classifying Lines
Positive Slope
Negative Slope
Slope of Zero
Undefined Slope
Example:
Find the Error:
Kate:
Kate and Dave are finding the slope of the line that passes
through (2,6) and (5,3).
3  6 3

5 2 3
Who is correct?

Dave:
63 3

52 3

4-1 Slope as a Rate of Change
Slope can be interpreted as the rate of change of a line. This means that slope tells us
how y changes as x increases. The change in y can be an increase (positive slope) or a
decrease (negative slope).
Example 1
The slope of this line is _____.
This means that y (increases or decreases)
____ unit(s) for every _____ unit(s) that x
increases.
Example 2
The slope of this line is _____.
This means that y (increases or decreases) ____ unit(s)
for every _____ unit(s) that x increases.
A graph may represent a real-world situation. The slope, or rate of change, will have
units of measurement that allow us to interpret the rate of change.
Example 1
The graph shows the distance traveled in miles
given the amount of time traveled in hours.
1) Write the slope as a rate of change.
2) Interpret the slope in the context of the problem.
Example 2
The graph shows the amount of water in
gallons that flows through two different
pipes after a certain number of minutes.
1) What is the flow rate of pipe A?
2) What is the flow rate of pipe B?
3) The flow rate of pipe A is greater than the flow rate of pipe B. How is that evident from
the graph?
Example 3
1) Explain what information the graph shows.
2) From 0 minutes to 400 minutes, the graph has a slope of 0.
Explain what this means in the context of the problem.
Example 4:
Naomi left from an elevation of 7400 feet at 7:00am and hiked to an elevation of 9800 feet
by 11:00am. What was her rate of change in altitude?
Section 4 - 4 Writing Equations in Slope Intercept Form
Remember:
Slope intercept form: ______________________
m =
b =
Example 1)
Find the linear equation given the slope and y-intercept.
1). Slope = -4 and y-intercept = 3
2). Slope =

Example 2)
Find the linear equations given a graph.
1)
2)
Steps: 1)
2)
3)
1
and y-intercept = -7
5
Example 3)
Writing linear equations give the slope and a point.
1) The slope is 3 and ordered pair (1, 4).
What is m =
What is x =
What is y =
Substitute into y = mx + b and solve for b.
2) The slope is
1
and ordered pair (-4, 10).
2

3) The slope is 
3
and ordered pair (5, 12).
5

3 5 
4) The slope is -3 and ordered pair  , .
2 2 

Example 4)
Writing linear equation given two points.
1) Given the ordered pairs ( 6, -6) and ( -4, -4).
Find the slope first m =
Pick one of the ordered pair to substitute into y = mx + b
Solve for b
2) Given the ordered pair ( -5, 4) and ( -5, -1).
3)
Given the ordered pair ( -2, 0) and ( 1, -1).
4) Given the ordered pair ( -2, 3) and ( 8, 3).
Section 4 – 3: Graphing Equations in Slope Intercept Form
y  mx  b
Slope-Intercept Form:
 m represents the slope of the line
 b represents the y-intercept of the line.
y – intercept (b) = is the point where the graph crosses the y – axis at the
point ( 0, y).

Example:
State the slope and y – intercept.
1) y  2x  6
2) y  3 x
3.)

Write Equation in Slope Intercept Form
1.)
2.)
3.)
4.)
Write and Equation from the Line and Points:
Write an Equation from the Line:
Graphing Linear Equations
Graph the following equations.
1)
y  3x  5
2)
y  2 x  4
3)
y
4)
y  3x 1
5)
y  2x  4
6)
y
1
x2
5



1
x 6
5
Section 4.5 Writing Equations in Point-Slope Form
Point – Slope Form:
y  y1  m(x  x1)
(x1, y1) is from given point

m is the slope of the line.

Example 1)
Write the point-slope form of an equation for the line that passes through (-1, 5) with
the slope of (-3).
Example 2)
Write y – 2 = 3(x + 5) in slope intercept form
Example 3)
Use the point slope formula to find the linear equations given two points.
***(Hint: First Find Slope)***
1) Given the ordered pairs ( 5, 1) and ( 8, -2)
2) Give the ordered pairs ( 6, 0) and ( 0, 4).
****Practice: Pg. 223 in Book
Section 4 -6 Line of Best Fit
Defintions:
Scatter Plot –
Line of Fit –
Best-Fit Line –
Example:
Negative Correlation
Post Correlation
Is this Correlation Positive or Negative?
a.
b.
Example 1.)
-
The Table shows the Largest vertical drops of nine roller coasters in the
United States and the number of years after 1988 that they were opened.
Years
1
Since
1988
Vertical 151
Drop
(ft)
3
5
8
12
12
12
13
15
155
225
230
306
300
255
255
400
a. Draw a scatter plot and determine what relationship exists, if any, in the data.
b. Draw a line of Fit
c. Write the slop intercept form of the equation
*** Using your equation what should the largest vertical drop be in 2014??***
Section 4 – 7 Parallel and Perpendicular Lines
Parallel Lines: Lines in the same plane that do not intersect.
*****Parallel Lines have the same Slope.******
Example:
y = 2x + 3 &
y = 2x -7
y
10
9
8
7
6
5
4
3
2
1
x
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
-1
1
2
3
4
5
6
7
8
9 10
-2
-3
-4
-5
-6
-7
-8
-9
-10
Write an equation for a line, given a point and the equation of a line parallel to it.
(Use point slope form, then write in slope intercept form)
1. The point (-1,-2) and parallel to y = -3x -2
2. The point (3,5) and parallel to 2x + 4y = 12 (solve for y first)
3. The point (-2,4) and parallel to y = 3
4. The point (-3,-5) and parallel to x = 1
Perpendicular Lines: Lines that intersect at right angles.
***Perpendicular Lines are Opposite Reciprocals*** ex: 4 = -1/4
Example:
y = 5/3x + 4 and y = -3/5x + 2
y
10
9
8
7
6
5
4
3
2
1
x
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
-1
1
2
3
4
5
6
7
8
9 10
-2
-3
-4
-5
-6
-7
-8
-9
-10
Write an equation for a line, given a point and the equation of a line perpendicular to
it
1. The point (-3,-2) and perpendicular to graph of y = ¼x + 3
2. The point (1,6) and perpendicular to graph of 4x – 2y = 6 (solve for y)
3. The point (5,-2) and perpendicular to graph of y = 3
4. The point (-4,0) and perpendicular to graph of x = -1
Determine whether two lines are perpendicular, parallel or neither
1. y =
4
x +3 and y = -3/4x -2
3
2. y =
1
x + 5 and y = -2x + 3
2


3. y = 2x + 6
and
-4x + 2y = 20
4. 4x + 8y = 2 and -x – 2y = 6
Concept Summary
Form
Equation
Forms of Linear Equations
Description
Slope-Intercept
Point-Slope
Example:
A line has a slope -2 and passes through the point (5, 3). Write the equation of the
line in:
a) Point-Slope form:
b) Slope-Intercept form: