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```									 7-7 Finding Slope of a Line

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Warm Up
California Standards
Lesson Presentation

Holt CA Course 1
7-7 Finding Slope of a Line

Warm Up
Evaluate each equation for x = –1, 0,
and 1.

1. y = 3x       –3, 0, 3
2. y = x – 7    –8, –7, –6
3. y = 2x + 5   3, 5, 7
4. y = 6x – 2   –8, –2, 4

Holt CA Course 1
7-7 Finding Slope of a Line

California
Standards
AF3.4 Plot the values of quantities
whose ratios are always the same (e.g.
cost to the number of an item, feet to
inches, circumference to diameter of a
circle). Fit a line to the plot and
understand that the slope of the line equals
the quantities.
Also covered:            AF3.3.

Holt CA Course 1
7-7 Finding Slope of a Line

Recall that lines have constant slope. For
a line on the coordinate plane, slope is
the following ratio:

vertical change    change in y
=
horizontal change   change in x

Holt CA Course 1
7-7 Finding Slope of a Line

If you know any two points on a line, you
can find the slope of the line without
graphing. The slope of a line through the
points (x1, y1) and (x2, y2) is as follows:

y2 – y1
slope =
x 2 – x1

When finding slope using the ratio above, it does
not matter which point you choose for (x1, y1)
and which point you choose for (x2, y2).

Holt CA Course 1
7-7 Finding Slope of a Line
Additional Example 1: Finding Slope, Given Two
Points
Find the slope of the line that passes through
A. (–2, –3) and (4, 6).
Let (x1, y1) be (–2, –3) and (x2, y2) be (4, 6).

y2 – y1 6 – (–3)     Substitute 6 for y2, –3 for y1,
x2 – x1 = 4 – (–2)   4 for x2, and –2 for x1.
= 6 + 2 =9
3
4+        6
=3       Simplify.
2
The slope of the line that passes through
(–2, –3) and (4, 6) is 3.
2

Holt CA Course 1
7-7 Finding Slope of a Line
Additional Example 1: Finding Slope, Given Two
Points
Find the slope of the line that passes through
B. (1, 3) and (2, 1).
Let (x1, y1) be (1, 3) and (x2, y2) be (2, 1).

y2 – y1 1 – 3         Substitute 1 for y2, 3 for y1,
x2 – x1 = 2 – 1       2 for x2, and 1 for x1.
-2          Simplify.
= 1 = –2

The slope of the line that passes through
(1, 3) and (2, 1) is –2.

Holt CA Course 1
7-7 Finding Slope of a Line
Additional Example 1: Finding Slope, Given Two
Points
Find the slope of the line that passes through
C. (3, –2) and (1, –2).
Let (x1, y1) be (3, –2) and (x2, y2) be (1, –2).
y2 – y1 –2 – (–2) Substitute -2 for y2, -2 for y1,
x2 – x1 = 1 – 3   1 for x2, and 3 for x1.
-2 + 2     Rewrite subtraction as addition of
=1–3      the opposite.
0
= –2 = 0
The slope of the line that passes through
(3, –2) and (1, –2) is 0.

Holt CA Course 1
7-7 Finding Slope of a Line
Check It Out! Example 1

Find the slope of the line that passes through
A. (–4, –6) and (2, 3).
Let (x1, y1) be (–4, –6) and (x2, y2) be (2, 3).

y2 – y1 3 – (–6)     Substitute 3 for y2, –6 for y1,
x2 – x1 = 2 – (–4)   2 for x2, and –4 for x1.
=9 =3
6    2
The slope of the line that passes through
(–4, –6) and (2, 3) is 3.
2

Holt CA Course 1
7-7 Finding Slope of a Line
Check It Out! Example 1
Find the slope of the line that passes through
B. (2, 4) and (3, 1).
Let (x1, y1) be (2, 4) and (x2, y2) be (3, 1).

y2 – y1 1 – 4         Substitute 1 for y2, 4 for y1,
x2 – x1 = 3 – 2       3 for x2, and 2 for x1.
-3          Simplify.
= 1 = –3

The slope of the line that passes through
(2, 4) and (3, 1) is –3.

Holt CA Course 1
7-7 Finding Slope of a Line
Check It Out! Example 1
Find the slope of the line that passes through
C. (3, –2) and (1, –4).
Let (x1, y1) be (3, –2) and (x2, y2) be (1, –4).
y2 – y1 –4 – (–2) Substitute -4 for y2, -2 for y1,
x2 – x1 = 1 – 3   1 for x2, and 3 for x1.

= –4 + 3
1–
2

= –2 = 1      Simplify.
–2
The slope of the line that passes through
(3, –2) and (1, –4) is –2.

Holt CA Course 1
7-7 Finding Slope of a Line
The table shows the total cost of fruit per pound
purchased at the grocery store. Use the data to
make a graph. Find the slope of the line and
explain what it shows.       Cost of Fruit
Graph the data.

Cost

Pounds

Holt CA Course 1
7-7 Finding Slope of a Line

You can use any two points to find the
slope of the line.

Holt CA Course 1
7-7 Finding Slope of a Line

Cost of Fruit
Find the slope of the line:
y2 – y1
x2 – x1

Cost
30 - 15        Substitute.
10 - 5

15 = 3       Multiply.
5
Pounds
The slope of the line is 3. This means that for every
pound of fruit, you will pay another \$3.

Holt CA Course 1
7-7 Finding Slope of a Line
Check It Out! Example 2
The table shows the total cost of gas per gallon.
Use the data to make a graph. Find the slope of
the line and explain what it shows.
Cost of Gas
Graph the data.          y

Cost of Gas          12

Gallons   Cost

Cost
9

0        0            6

3        6
3
6       12
0    3   6   9   x
Gallons

Holt CA Course 1
7-7 Finding Slope of a Line
Check It Out! Example 2 Continued
Cost of Gas
Find the slope of the line:              y

y2 – y1                         12

x2 – x1 =

Cost
9
12 - 6       Substitute.
6-3                             6

6       = 2 Multiply.           3
3
0        3   6   9   x
Gallons
The slope of the line is 2. This means that for every
gallon of gas, you will pay another \$2.

Holt CA Course 1
7-7 Finding Slope of a Line

The slope of a line may be positive, negative,
zero, or undefined. You can tell which of these
is the case by looking at the graphs of a line—
you do not need to calculate the slope.

Holt CA Course 1
7-7 Finding Slope of a Line

Holt CA Course 1
7-7 Finding Slope of a Line

Holt CA Course 1
7-7 Finding Slope of a Line
Lesson Quiz: Part I

Find the slope of the line that passes
through each pair of points.
1. (4, 3) and (–1, 1)    2
5

2. (–1, 5) and (4, 2)   –3
5

Holt CA Course 1
7-7 Finding Slope of a Line
Lesson Quiz: Part II
3. The table shows how much money Susan earned
as a house painter for one afternoon. Use the
data to make a graph. Find the slope of the line
and explain what it shows. y
The slope of the line is 7.
This means Susan earned       80
\$7 for each hour worked.      70
60
50
40
30
20
10
x
0    2   4 6 8 10 12 14

Holt CA Course 1

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