confidential 1 algebra1 the slope formula. confidential 2 warm up tell whether the given ordered...
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![Page 1: CONFIDENTIAL 1 Algebra1 The Slope Formula. CONFIDENTIAL 2 Warm Up Tell whether the given ordered pairs satisfy a linear function. 1) {(1, 1), (2, 4),](https://reader036.vdocument.in/reader036/viewer/2022081520/5697bf891a28abf838c8a3ef/html5/thumbnails/1.jpg)
CONFIDENTIAL 1
Algebra1Algebra1
The Slope The Slope FormulaFormula
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CONFIDENTIAL 2
Warm UpWarm Up
Tell whether the given ordered pairs satisfy a linear function.
1) {(1, 1) , (2, 4) , (3, 9) , (4, 16)}
2) {(9, 0), (8, -5), (5, -20), (3, -30)}
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CONFIDENTIAL 3
The Slope Formula
In the previous lesson, slope was described asthe constant rate of change of a line. You saw how to
find the slope of a line by using its graph.
There is also a formula you can use to find the slope of a line, which is usually represented by the letter m. To use this formula, you need the coordinates of two
different points on the line.
WORDS FORMULA EXAMPLE
The slope of a line is the ratio of the
difference in y-values to the difference in x-values between any
two different points on the line.
If (x1 , y1) and (x2 , y2) are any two
different points on a line, the slope of
the line is m = y2 – y1 x2 – x1
If (2, -3) and (1, 4) are two points on a line,
the slope of the line ism = 4 – (-3) = 7 = -7 1 – 2 -1
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CONFIDENTIAL 4
1) Find the slope of the line that contains (4, -2) and (-1, 2).
Finding Slope by Using the Slope Formula
m = y2 – y1 x2 – x1
Use the slope formula.
Substitute (4, -2) for ( x1 , y1 ) and (-1, 2) for ( x2 , y2 ) .
Simplify.
= 2 – (-2) -1 – 4
= 4 -5
= -4 5
The slope of the line that contains ( 4, -2) and (-1, 2) is -4. 5
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CONFIDENTIAL 5
Now you try!
1a) Find the slope of the line that contains (-2, -2) and (7, -2).
1a) Find the slope of the line that contains (5, -7) and (6, -4).
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CONFIDENTIAL 6
Sometimes you are not given two points to use in the formula. You might have to choose
two points from a graph or a table.
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CONFIDENTIAL 7
Finding Slope from Graphs and Tables2a) Each graph or table shows a linear relationship. Find the slope.
m = y2 – y1 x2 – x1
Use the slope formula.
Substitute (2, 2) for ( x1 , y1 ) and (-2, -1) for ( x2 , y2 ) .
Simplify.
= -1 – 2 -2 – 2
= -3 -4= 3 4
Let (2, 2) for ( x1 , y1 ) and (-2, -1) for ( x2 , y2 ) .
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CONFIDENTIAL 8
Finding Rates of Change from a Graph
2b) Each graph or table shows a linear relationship. Find the slope.
Step1: Choose any two points from the table. Let (2, 0) be (x1 , y1 ) and (2, 3) be (x2 , y2).
Step2: Use the slope formula.
m = y2 – y1 x2 – x1
Use the slope formula.
Substitute (2, 0) for ( x1 , y1 ) and (2, 3) for ( x2 , y2 ) .
Simplify.
= 3 – 0 2 – 2
= 3 0
The slope is undefined.
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CONFIDENTIAL 9
Now you try!
Each graph or table shows a linear relationship. Find the slope.
2a) 2a)
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CONFIDENTIAL 10
Remember that slope is a rate of change. In real-world problems, finding the slope can give you
information about how quantity is changing.
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CONFIDENTIAL 11
The graph shows how much water is in a reservoir at different times. Find the slope of the line. Then tell what
the slope represents.
Application
Next slide
Step1: Use the slope formula.
m = y2 – y1 x2 – x1
= 2000 – 3000 60 – 20
= -1000 40
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CONFIDENTIAL 12
A slope of -25 means the amount of water in the reservoir is decreasing (negative change) at a rate of
25 thousand cubic feet each hour.
Step2: Tell what the slope represents.
In this situation, y represents volume of water and x represents time.
So slope represents change in volume change in time
thousands_of cubic_fee_ change in time
in units of
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CONFIDENTIAL 13
3) The graph shows the height of a plant over a period of days. Find the slope of the line. Then tell
what the slope represents.
Now you try!
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CONFIDENTIAL 14
If you know the equation that describes a line, you can find its slope by using any two ordered-pair solutions. It is often easiest to use the ordered
pairs that contain the intercepts.
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CONFIDENTIAL 15
Finding Slope from an Equation
4) Find the slope of the line described by 6x - 5y = 30.
Step1: Find the x-intercept.
6x - 5y = 30
6x - 5 (0) = 30 Let y = 0.
6x = 30
6x = 30 6 6
x = 5
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CONFIDENTIAL 16
Step2: Find the y-intercept.
6x - 5y = 30
6 (0) - 5y = 30 Let x = 0.
-5y = 30
-5y = 30 5 5
y = -6
Step1: The line contains (5, 0) and (0, - 6) . Use the slope formula.
m = y2 – y1 = - 6 – 0 = -6 = 6 x2 – x1 0 – 5 -5 5
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CONFIDENTIAL 17
4) Find the slope of the line described by 2x + 3y = 12.
Now you try!
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CONFIDENTIAL 18
Assessment
1) (3, 6) and (6, 9)
Find the slope of the line that contains each pair of points.
2) 3, 7 and 1, 2 4 5 4 5
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CONFIDENTIAL 19
Each graph or table shows a linear relationship. Find the slope.
3) 4)
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CONFIDENTIAL 20
5) 6)
Find the slope of each line. Then tell what the slope represents.
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CONFIDENTIAL 21
7) 8x + 2y = 96
8) 5x = 90 - 9y
Find the slope of the line described by each equation.
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CONFIDENTIAL 22
9) The equation 2y + 3x = -6 describes a line with what slope?
10) A line with slope – 1 could pass through which 3
of the following pairs of points?
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CONFIDENTIAL 23
The Slope Formula
In the previous lesson, slope was described asthe constant rate of change of a line. You saw how to
find the slope of a line by using its graph.
There is also a formula you can use to find the slope of a line, which is usually represented by the letter m. To use this formula, you need the coordinates of two
different points on the line.
WORDS FORMULA EXAMPLE
The slope of a line is the ratio of the
difference in y-values to the difference in x-values between any
two different points on the line.
If (x1 , y1) and (x2 , y2) are any two
different points on a line, the slope of
the line is m = y2 – y1 x2 – x1
If (2, -3) and (1, 4) are two points on a line,
the slope of the line ism = 4 – (-3) = 7 = -7 1 – 2 -1
Let’s review
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CONFIDENTIAL 24
1) Find the slope of the line that contains (4, -2) and (-1, 2).
Finding Slope by Using the Slope Formula
m = y2 – y1 x2 – x1
Use the slope formula.
Substitute (4, -2) for ( x1 , y1 ) and (-1, 2) for ( x2 , y2 ) .
Simplify.
= 2 – (-2) -1 – 4
= 4 -5
= -4 5
The slope of the line that contains ( 4, -2) and (-1, 2) is -4. 5
![Page 25: CONFIDENTIAL 1 Algebra1 The Slope Formula. CONFIDENTIAL 2 Warm Up Tell whether the given ordered pairs satisfy a linear function. 1) {(1, 1), (2, 4),](https://reader036.vdocument.in/reader036/viewer/2022081520/5697bf891a28abf838c8a3ef/html5/thumbnails/25.jpg)
CONFIDENTIAL 25
Finding Slope from Graphs and Tables2a) Each graph or table shows a linear relationship. Find the slope.
m = y2 – y1 x2 – x1
Use the slope formula.
Substitute (2, 2) for ( x1 , y1 ) and (-2, -1) for ( x2 , y2 ) .
Simplify.
= -1 – 2 -2 – 2
= -3 -4= 3 4
Let (2, 2) for ( x1 , y1 ) and (-2, -1) for ( x2 , y2 ) .
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CONFIDENTIAL 26
Finding Rates of Change from a Graph
2b) Each graph or table shows a linear relationship. Find the slope.
Step1: Choose any two points from the table. Let (2, 0) be (x1 , y1 ) and (2, 3) be (x2 , y2).
Step2: Use the slope formula.
m = y2 – y1 x2 – x1
Use the slope formula.
Substitute (2, 0) for ( x1 , y1 ) and (2, 3) for ( x2 , y2 ) .
Simplify.
= 3 – 0 2 – 2
= 3 0
The slope is undefined.
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CONFIDENTIAL 27
The graph shows how much water is in a reservoir at different times. Find the slope of the line. Then tell what
the slope represents.
Application
Next slide
Step1: Use the slope formula.
m = y2 – y1 x2 – x1
= 2000 – 3000 60 – 20
= -1000 40
![Page 28: CONFIDENTIAL 1 Algebra1 The Slope Formula. CONFIDENTIAL 2 Warm Up Tell whether the given ordered pairs satisfy a linear function. 1) {(1, 1), (2, 4),](https://reader036.vdocument.in/reader036/viewer/2022081520/5697bf891a28abf838c8a3ef/html5/thumbnails/28.jpg)
CONFIDENTIAL 28
A slope of -25 means the amount of water in the reservoir is decreasing (negative change) at a rate of
25 thousand cubic feet each hour.
Step2: Tell what the slope represents.
In this situation, y represents volume of water and x represents time.
So slope represents change in volume change in time
thousands_of cubic_fee_ change in time
in units of
![Page 29: CONFIDENTIAL 1 Algebra1 The Slope Formula. CONFIDENTIAL 2 Warm Up Tell whether the given ordered pairs satisfy a linear function. 1) {(1, 1), (2, 4),](https://reader036.vdocument.in/reader036/viewer/2022081520/5697bf891a28abf838c8a3ef/html5/thumbnails/29.jpg)
CONFIDENTIAL 29
Finding Slope from an Equation
4) Find the slope of the line described by 6x - 5y = 30.
Step1: Find the x-intercept.
6x - 5y = 30
6x - 5 (0) = 30 Let y = 0.
6x = 30
6x = 30 6 6
x = 5
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CONFIDENTIAL 30
Step2: Find the y-intercept.
6x - 5y = 30
6 (0) - 5y = 30 Let x = 0.
-5y = 30
-5y = 30 5 5
y = -6
Step1: The line contains (5, 0) and (0, - 6) . Use the slope formula.
m = y2 – y1 = - 6 – 0 = -6 = 6 x2 – x1 0 – 5 -5 5
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CONFIDENTIAL 31
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