1. Preview
Warm Up
California Standards
Lesson Presentation

2. Warm Up
Evaluate 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

3. 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.

4. vertical change horizontal change
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 =

5. 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
x2 – x1
slope =
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).

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

7. 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
x2 – x1
1 – 3
2 – 1
Substitute 1 for y2, 3 for y1,
2 for x2, and 1 for x1. -2 1 =
= –2
Simplify.
The slope of the line that passes through (1, 3) and (2, 1) is –2.

8. 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
x2 – x1
–2 – (–2)
1 – 3
Substitute -2 for y2, -2 for y1,
1 for x2, and 3 for x1.
-2 + 2
1 – 3 =
Rewrite subtraction as addition of the opposite.
= 0 –2 =
The slope of the line that passes through (3, –2) and (1, –2) is 0.

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

10. 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
x2 – x1
1 – 4
3 – 2
Substitute 1 for y2, 4 for y1,
3 for x2, and 2 for x1. -3 1 =
= –3
Simplify.
The slope of the line that passes through (2, 4) and (3, 1) is –3.

11. 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
x2 – x1
–4 – (–2)
1 – 3
Substitute -4 for y2, -2 for y1,
1 for x2, and 3 for x1.
–4 + 2
1 – 3 =
= 1 –2 =
Simplify.
The slope of the line that passes through (3, –2) and (1, –4) is –2.

12. Additional 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.
Pounds
Cost
Cost of Fruit
Graph the data.

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

14. Additional Example 2 Continued
Pounds
Cost
Cost of Fruit
Find the slope of the line:
y2 – y1
x2 – x1
10 - 5
Substitute. 15 5
= 3
Multiply.
The slope of the line is 3. This means that for every pound of fruit, you will pay another $3.

15. Cost of Gas Gallons Cost
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. 6 9 12 3 x y
Gallons
Cost of Gas
Cost
Graph the data.
Cost of Gas
Gallons
Cost 3 6 12

16. Check It Out! Example 2 Continued6 9 12 3 x y
Gallons
Cost of Gas
Cost
Find the slope of the line: =
y2 – y1
x2 – x1
12 - 6
6 - 3
Substitute. 6 3
= 2
Multiply.
The slope of the line is 2. This means that for every gallon of gas, you will pay another $2.

17. The slope of a line may be positive, negative, zero, or undefined
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.

20. 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) 2 5 5 3 –

21. 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. x y 6 4 2 8 10 12 14 20 30 40 50 60 70 80
The slope of the line is 7. This means Susan earned $7 for each hour worked.