algebra 4.4 slope. finding slope m = slope = rise run = change in y change in x y 2 – y 1 = x 2...
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Algebra
4.4 Slope
Finding Slope
m = slope
= rise
run
= change in y
change in x
y2 – y1=
x2 – x1
x
y
..
(x1 , y1)
(x2 , y2)
The order the arcs subtract does not matter, as long as the order is the same for both!
Find the slope of the line.
4 – 2=
3 – (-2)x
y ..(-2 , 2)
(3 , 4)
y2 – y1=
x2 – x1
slope
2=
3 + 2
2=
5 The slope of the line is 2/5.
You try! Find the slope of the line.
1 – (-5)=
-2 – 1x
y
.
.(-2 , 1)
(1 , -5)
y2 – y1=
x2 – x1
slope
1 + 5=
-3
=
-3 The slope of the line is -2.6
Can you simplify slope? Yes!
Try another. Find the slope of the line.
2 – 2=
3 – (-1)x
y
..(-1 , 2) (3 , 2)
y2 – y1=
x2 – x1
slope
0=
3 + 1
=
4 The slope of the line is 0.0
All horizontal lines have a zero slope.
It’s like jogging on flat ground, your slope is zero.
How about the slope between (2, 1) and (2, 4)?
4 – 1=
2 - 2
y2 – y1=
x2 – x1
slope
3=
0The slope of the line is undefined.All vertical lines have an undefined slope.
It’s like going up in an elevator, your rise can beanything, but your run is zero.
x
y
.
.(2 , 1)
(2 , 4)
Every type of slope.Positive SlopeGreater than 1
Uphill
Steep
Positive SlopeLess than 1
Uphill
Flatter
Negative SlopeGreater than 1
Downhill
Steep
Negative SlopeLess than 1
Downhill
Flatter
Slope = 0
Undefined Slope
Running up the hill is undefined!
Identifying a Slope of -3.
Is it uphill or downhill?
Downhill
Is it steep or flatter?
Steep
Rise -3
Run 1
Identifying a Slope of 1/4.
Is it uphill or downhill?
Uphill
Is it steep or flatter?
Flatter
Rise 1
Run 4
Identifying a Slope of -2/3.
Is it uphill or downhill?
Downhill
Is it steep or flatter?
Flatter
Rise -2
Run 3
Find the value of y so that the line passing through the points (-2, 1) and (4, y) and has a slope of 2/3.
y – 1=
4 – (-2)
y2 – y1=
x2 – x1
slope
y - 1=
6
= y - 1
32
32 Clear the fraction by multiplying by the LCD66
4= y 5
Find the value of y so that the line passing through the points (3, y) and (5, 8) and has a slope of 2.
8 – y=
5 – 3
y2 – y1=
x2 – x1
slope
8 - y=
2
= 8 - y
2
2 Multiply each side by 2.22
4= - y -4 = y 4
Homework
P. 230 #13 -19 Odd (graph, no graph paper required)
# 21 - 41 Odd (calculate, do not graph)