Holt CA Course 1
7-7 Finding Slope of a Line
Warm UpWarm Up
California StandardsCalifornia Standards
Lesson Presentation
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Holt CA Course 1
7-7 Finding Slope of a Line
Warm UpEvaluate each equation for x = –1, 0, and 1.
1. y = 3x
2. y = x – 7
3. y = 2x + 5
4. y = 6x – 2
–3, 0, 3
–8, –7, –6
3, 5, 7
–8, –2, 4
Holt CA Course 1
7-7 Finding Slope of a Line
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.
California Standards
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 horizontal change
change in y 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:
yy22 –– yy11 xx22 –– xx11
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).
slope =
Holt CA Course 1
7-7 Finding Slope of a Line
Find the slope of the line that passes through A. (–2, –3) and (4, 6).
Additional Example 1: Finding Slope, Given Two Points
Let (x1, y1) be (–2, –3) and (x2, y2) be (4, 6).
6 – (–3)4 – (–2)
Substitute 6 for y2, –3 for y1, 4 for x2, and –2 for x1.
6 + 34 + 2=
The slope of the line that passes through (–
2, –3) and (4, 6) is . 32
=y2 – y1
x2 – x1
96=
Simplify.32=
Holt CA Course 1
7-7 Finding Slope of a Line
Find the slope of the line that passes through B. (1, 3) and (2, 1).
Additional Example 1: Finding Slope, Given Two Points
Let (x1, y1) be (1, 3) and (x2, y2) be (2, 1).
1 – 32 – 1
Substitute 1 for y2, 3 for y1, 2 for x2, and 1 for x1.
2 1=
The slope of the line that passes through
(1, 3) and (2, 1) is –2.
=y2 – y1
x2 – x1
= –2 Simplify.
Holt CA Course 1
7-7 Finding Slope of a Line
Find the slope of the line that passes through C. (3, –2) and (1, –2).
Additional Example 1: Finding Slope, Given Two Points
Let (x1, y1) be (3, –2) and (x2, y2) be (1, –2).
–2 – (–2) 1 – 3
Substitute 2 for y2, 2 for y1, 1 for x2, and 3 for x1.
2 + 2 1 – 3 =
The slope of the line that passes through
(3, –2) and (1, –2) is 0.
=y2 – y1
x2 – x1
= 0
Rewrite subtraction as addition of the opposite.
0 –2=
Holt CA Course 1
7-7 Finding Slope of a Line
Find the slope of the line that passes through A. (–4, –6) and (2, 3).
Check It Out! Example 1
Let (x1, y1) be (–4, –6) and (x2, y2) be (2, 3).
3 – (–6)2 – (–4)
Substitute 3 for y2, –6 for y1, 2 for x2, and –4 for x1.
96=
The slope of the line that passes through (–
4, –6) and (2, 3) is . 32
=y2 – y1
x2 – x1
32=
Holt CA Course 1
7-7 Finding Slope of a Line
Find the slope of the line that passes through B. (2, 4) and (3, 1).
Check It Out! Example 1
Let (x1, y1) be (2, 4) and (x2, y2) be (3, 1).
1 – 43 – 2
Substitute 1 for y2, 4 for y1, 3 for x2, and 2 for x1.
3 1=
The slope of the line that passes through
(2, 4) and (3, 1) is –3.
=y2 – y1
x2 – x1
= –3 Simplify.
Holt CA Course 1
7-7 Finding Slope of a Line
Find the slope of the line that passes through C. (3, –2) and (1, –4).
Check It Out! Example 1
Let (x1, y1) be (3, –2) and (x2, y2) be (1, –4).
–4 – (–2) 1 – 3
Substitute 4 for y2, 2 for y1, 1 for x2, and 3 for x1.
–4 + 2 1 – 3 =
The slope of the line that passes through
(3, –2) and (1, –4) is –2.
=y2 – y1
x2 – x1
Simplify.= 1 –2 –2=
Holt CA Course 1
7-7 Finding Slope of a LineAdditional Example 2: Money Application
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.
Graph the data.
Pounds
Cost
Cost of Fruit
Holt CA Course 1
7-7 Finding Slope of a Line
You can use any two points to find the slope of the line.
Helpful Hint
Holt CA Course 1
7-7 Finding Slope of a LineAdditional Example 2 Continued
Find the slope of the line:
The slope of the line is 3. This means that for every pound of fruit, you will pay another $3.
y2 – y1
x2 – x1
15 5
30 15 10 5
= 3Pounds
Cost
Cost of Fruit
Substitute
Multiply
Holt CA Course 1
7-7 Finding Slope of a LineCheck 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.
Graph the data.
Cost of Gas
Gallons Cost
0 0
3 6
6 12
6
9
9
12
6 0
3
3 x
y
Gallons
Cost of Gas
Cost
Holt CA Course 1
7-7 Finding Slope of a Line
Check It Out! Example 2 Continued
Find the slope of the line:
The slope of the line is 2. This means that for every gallon of gas, you will pay another $2.
=y2 – y1
x2 – x1
6 3
12 6 6 3
= 2
6
9
9
12
6 0
3
3 x
y
Gallons
Cost of Gas
Cost
Substitute.
Multiply.
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. (–1, 5) and (4, 2)
25
53–
Holt CA Course 1
7-7 Finding Slope of a LineLesson 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.
x
y
64 2 8 10 12 14 0
10
20
30
40
50
60
7080
The slope of the line is 7. This means Susan earned $7 for each hour worked.