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Slope (Algebra)
What is slope?
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Types of Slope
Imagine that you are walking to the right on a line.
A positive slope means that you are walking uphill.
Types of Slope
Imagine that you are walking to the right on a line.
A negative slope means that you are walking downhill.
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Types of Slope
Imagine that you are walking to the right on a line.
Zero slope means that you are walking on level ground.
Types of Slope
Undefined slope is a vertical line. You can not walk
up a vertical line. It is not possible. You would fall!
ouch!
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y-axis
Quadrant II
Positive
Let’s review…
Positive
Negative
Negative
Quadrant III
Quadrant I
x-axis
Quadrant IV
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How do you calculate slope?
Slope is a ratio and represented by the
variable m.
One way to figure out slope is remember the ratio
rise over run:
vertical rise
slope (m) =
horizontal run
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When you are given points on a line,
you can calculate the slope by the
following steps:
1. Write slope ratio.
m=
rise
run
2. Start at one point & find the
vertical rise to the other
point.
3. Start at the same point
again and find the horizontal
run.
4. Simplify
Steps to find the slope- Example 1
1. Write slope ratio.
2. Start at point A
& find the
vertical rise to
point B.
m=
=
rise
run
4
−2
3. Find the
horizontal run.
4. Simplify
y
•
B
= −2
x
•
A
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Example 2
Find the slope of the line.
1. Write slope ratio.
2. Start at either
point. Find the
vertical rise.
m=
rise
run
==
4
7
y
•
3. Find the
horizontal run.
•
x
When simplifying slope….
NEVER
change an improper
fraction to a mix number. Why?
m=
3
2
x
m =1
1
2
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Example 3 Find the slope of the line.
1. Write slope ratio.
m=
2. Start at either
point. Find the
vertical rise.
3. Find the
horizontal run.
4. Simplify
=
rise
run
0
5
=0
y
•
•
x
zero ooooover the
denominator
(zeroooooo slope)
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Example 4 Find the slope of the line.
1. Write slope ratio.
2. Start at either
point. Find the
vertical rise.
m=
=
3. Find the
horizontal run.
4. Simplify
rise
run
4
0
undefined
y
•
•
x
zero unnnnder the
numerator
(unnnnndefined slope)
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Another way to calculate slope…
slope is a rate of change =
m =
change of y
change of x
rise
change in y
=
run change in x
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When you are given ordered pairs, you can calculate the
slope by the following steps:
1. Stack the points
rise
change in y
=
= runthe
= formula
2. m
Write
change in x
change in y
change in x
3. Substitute numbers
for your variables
4. Solve & simplify
Example 1 Find the slope of the line that passes through
the points (2,4) and (-1,5).
1. Stack the points
( 2, 4 )
(− 1,5)
2. Write the formula
3. Substitute numbers
for your variables
4. Solve & simplify
=
=
4−5
2 − (− 1)
−1
3
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Example 2 Find the slope of the line that passes through
the points (8,4 ) and (3,2).
1. Stack the points
(8,4 )
(3,2)
2. Write the formula
3. Substitute numbers
for your variables
=
4 −2
8−3
4. Solve & simplify
=
2
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Example 3 Find the slope of the line that passes through
the points(5,−3) and (− 1,−3).
1. Stack the points
( 5,−3)
(− 1,−3)
2. Write the formula
3. Substitute numbers
for your variables
4. Solve & simplify
=
− 3 − (− 3)
5 − (− 1)
=
0
6
=0
Zero
oooooover
the line
(zeroooooo
slope)
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PRACTICE. Plot the points and draw the line that passes
through them. Without finding the slope, determine
whether the slope is positive, negative, zero, or undefined.
3. (4,5) and (2,2)
5. (2,2) and (–1,4)
4. (6,1) and (– 4,1)
6. (3,6) and (3,–1)
Find the slope by walking the line.
y
7.
y
8.
•
•
x
x
•
•
PRACTICE. Plot the points and draw the line that passes
through them. Without finding the slope, determine
whether the slope is positive, negative, zero, or undefined.
3. (4,5) and (2,2) positive 4. (6,1) and (– 4,1) zero
5. (2,2) and (–1,4) negative 6. (3,6) and (3,–1) undefined
Find the slope by walking the line.
y
7.
6
=2
3
•
y
8.
•
x
•
−
•
2
5
x
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Practice Problems
Find the slope using the slope formula.
1. (4,5) and (2,2) 3
2) (6,1) and (– 4,1) 0
2
2
3. (2,2) and (–1,4)
4) (3,6) and (3,–1) undefined
−
3
5. (2,-1) and (3,4)
6) (-3,-7) and (3,-7) 0
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• Watch Video:
• https://www.youtube.com/watch?v=9lfN2k
a-WNg
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