slope & y-intercept
Edited version of
kballard @ math.weebly.com
Vocabulary
• A rate of change is a ratio that compares the
amount of change of a dependent variable to
the independent variable.
• Slope: the steepness of a line described by
rate of change of y and x.
Steepness of Lines
• The slope of a line is a measure of its steepness.
• Use absolute value to compare the steepness of
multiple lines.
What is slope?
What does slope look like?
• There are four types of slope that describe the rate
of change.
• Using this will help you check your work and describe your
linear equation.
Slope Formula
• If you do not have a graph, but want to find
the slope, you can use two points in the slope
formula.
1) Substitute in both points
2) Subtract and simplify
Slope-Intercept Form
• The linear equation y = mx + b is written in
slope-intercept form.
• x and y stand for any x and y value.
• m is the slope (rise over run)
• b is the y-intercept (on the y-axis)
y = mx + b
Identify slope and y-intercept
1) y = 4x + 5
y= mx + b
2) y = ½ x – 7
m is always slope
b is always the y-intercept 3) y = x – ¾
4) y = -x + 3
Look at each equation
and determine the slope 5) y = x
value and the yintercept value.
6) y = 4
Identify slope and y-intercept
y = mx + b
If you have the graph,
1) Find the yintercept
2) Count rise over
run
3) Write the
Write the linear equation.
• Write the equation
in slope-intercept
form.
• y = mx + b
Graphing a line.
• Slope-intercept
form is the easiest
way to graph a line
when you have an
equation.
• It is the main way
that lines are
expressed.
Examples
Describing Slope -EX
• Tell whether the slope of each line is positive,
negative, zero, or undefined.
Finding Slope from a Graph-Ex
• To find the slope from a graph,
RISE( y )
m
RUN( x)
1) Pick any two points on the line.
2) Count RISE over RUN and simplify
Practice
• Name the type of slope and find the slope.
Special Cases
Practice
• Find the slope of each line.
Slope Formula-EX
Practice
Graph Lines #1
• How will we graph
a line when we
have y=mx + b?
Example: y = 2/3x - 4
m= _____ b =
_______
1) Plot the yintercept
2) Use your slope to
Graph Lines #2
• How will we graph
a line when we
have y=mx + b?
Example: y = -3x + 2
m= _____ b =
_______
1) Plot the yintercept
2) Use your slope to
Graph Lines #3
• How will we graph
a line when we
have y=mx + b?
Example: y = 1
m= _____ b =
_______
1) Plot the yintercept
2) Use your slope to
Graph Lines #4
• How will we graph
a line when we
have y=mx + b?
Example: x = -3
m= _____ b =
_______
1) Plot the yintercept
2) Use your slope to
Graph Lines
•
Identify the slope and y-intercept,
then graph the linear equation.
1)
2)
3)
4)
y = 2x + 3
y = -½x - 1
y = 5/6x + 8
y=x -7
REVIEW
1)
2)
3)
4)
5)
6)
7)
What is rate of change?
What is slope?
What are the four types of slope?
What does “rise” represent?
What does “run” represent?
How do you find slope from a graph?
What is the slope formula?
Review
1) What is slope-intercept form?
2) What do m and b represent?
3) How do you graph a line with slope-intercept
form?
4) What are the two special cases?
MATH HUMOR
• How are linear functions similar to Cupid?
– They have a partner for every number.
• Teacher: Where’s the graph of your function?
– Student: It was intercepted on the way to school.
• Why were the math students getting up and
sprinting around the classroom?
– Their teacher kept saing “rise” and “run”
• Why was the scientist smiling as he worked?
– His graph had a great plot!