4-1b the slope formula first a quick review of the types of slope! algebra 1 glencoe...
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4-1B The Slope Formula
First a quick review of the types of slope!
Algebra 1 Glencoe McGraw-Hill Linda Stamper
Types of SlopeImagine that you are walking to the right on a
line.A positive slope means that you are walking uphill.
Imagine that you are walking to the right on a line.A negative slope means that you are walking downhill.
Types of Slope
Imagine that you are walking to the right on a line. Zero slope means that you are walking on level ground.
Do not identify this as “no slope”.
Types of Slope
Undefined slope is a vertical line. You can not walk up a vertical line. It is not possible. You would fall!
Do not identify this as “no slope”.
ouch!
Types of Slope
In the previous lesson you determined slope by plotting the points on a coordinate plane and then calculating the ratio of rise to run.
Find the slope of the line.
4 74
It does not matter at which point you begin the walk!
x
yrunrise
m
•
•
What do you already
know about the sign of
the answer?
Today you will find slope using ordered pairs in the slope formula.
runrise
m
x change in y change in
m
12
12
xxyy
m
Let m = slope.
Find the slope of the line.
74
x
yrunrise
m
•
• 0,3
4,412
12
xxyy
m
11 y,x
22 y,x
.y,x and ,yx as point either label can You 2211
y,x
y,x
After labeling the points, you must subtract the coordinates in the same order in both the numerator and the denominator.
0
4
3
4
74
74
54
Find the slope of the line that passes through the points .5,1 and 4,2
Write the formula.
Substitute.
12
12
xxyy
m
Simplify.31
Stack the points.
12
22 y,x
11 y,x
5,1
4 ,2
.y,x and ,yx as point either label can You 2211
31
Stacking method from JoAnn Evans (Redwood).
Slope is a numerical
value!
All your problems
MUST start with the
slope formula!
Place the negative
sign before the fraction.
Find the slope of the line that passes through the given points
2,3 and 4,8Example 1
Example 2 3,1 and 3,5
Example 3 1,5 and 3,5
Example 4 .1,2 and 3,1
24
Example 1 Find the slope of the line that passes through the points .2,3 and 4,8
Write the formula.
Substitute.
12
12
xxyy
m
Simplify.
52
Stack the points.
38
22 y,x
11 y,x
2,3
4,8
Slope is a numerical
value!
33
Example 2 Find the slope of the line that passes through the points .3,1 and 3,5
12
12
xxyy
m
60
15
22 y,x
11 y,x
3,1
3,5
Zero oooooover the fraction
line is zeroooooo.
0
13
Example 3 Find the slope of the line that passes through the points .1,5 and 3,5
12
12
xxyy
m
04
55
22 y,x
11 y,x
1,5
3 ,5
undefined Zero unnnnder the fraction
line is unnnnndefi
ned.
Slope is a word!
13
Example 4 Find the slope of the line that passes through the points .1,2 and 3,1
12
12
xxyy
m
34
21
22 y,x
11 y,x
1 ,2
3 ,1
34
Place the negative
sign before the
fraction.
Slope is a numerical
value!
Given the slope of a line and one point on the line, you can find other points on the line.
Find the value of r so that the line through (r,4) and
(-3,0) has a slope of .
x
y
•
•
74
You are to find the x-
coordinate. The graph will NOT
be given!
Find the value of r so that the line through (r,4) and
(-3,0) has a slope of .
0,3
4,r
04
12
12
xxyy
m
74
3r
22 y,x
11 y,x
The slope is given!
74
Undo double sign.
3r 04
74
Use cross products
to solve.
4712r4 2812r4
12 1216r4
0473r4
4r
Write the formula.
Substitute.
Stack the points.
Find the value of r so the line that passes through each pair of points has the given slope.
Example 5 (1,4) and (-1,r) has a slope of 2Example 6 (r,2) and (6,3) has a slope of
21
11 r4
2
12
12
xxyy
m
22 y,x
11 y,x
r ,1
4 ,1
Example 5 Find the value of r so that the line through (1,4) and (-1,r) has a slope of 2.
2 r4
2
22
r4 22
r44 44r0
11 r4
2
6r 32
21
12
12
xxyy
m
22 y,x
11 y,x
3,6
2,r
Example 6 Find the value of r so that the line through
(r,2) and (6,3) has a slope of . 21
26r
6r 1
21
6 64r
126r1
Practice Problems
Find the slope using the slope formula.
1. (4,5) and (2,2) 2) (6,1) and (– 4,1)
3. (2,2) and (–1,4) 4) (3,6) and (3,–1)
5. (2,-1) and (3,4) 6) (-3,-7) and (3,-7)
23 0
32
undefined
05
4-A3 Page 193-195 # 20-39,64-65,68-71.