1. Slope of a Line 12-2 Learn to find the slope of a line and use slope to understand and draw graphs.

2. Slope of a Line 12-2 The constant rate of change of a line is called the slope of the line.

3. Slope of a Line 12-2 (5, 4) (1, 2) Then count horizontally to the second point to find the run. Find the slope of the line. Begin at one point and count vertically to find the rise. Additional Example 1: Finding the Slope of a Line slope = = 2424 1212 The slope of the line is. 1212

4. Slope of a Line 12-2 (3, 2) (–1, –2) Then count horizontally to the second point to find the run. Find the slope of the line. Begin at one point and count vertically to find the rise. Check It Out: Example 1 slope = = 1 4444 The slope of the line is 1.

5. Slope of a Line 12-2 If you know any two points on a line, or two solutions of a linear equation, you can find the slope of the line without graphing. The slope m of a line through the points (x 1, y 1 ) and (x 2, y 2 ) is as follows: y2 – y1y2 – y1x2 – x1x2 – x1y2 – y1y2 – y1x2 – x1x2 – x1 m =

6. Slope of a Line 12-2 Find the slope of the line that passes through (–2, –3) and (4, 6). Additional Example 2: Finding Slope, Given Two Points Let (x 1, y 1 ) be (–2, –3) and (x 2, y 2 ) be (4, 6). 6 – (–3) 4 – (–2) Substitute 6 for y 2, –3 for y 1, 4 for x 2, and –2 for x 1. 9 6 = The slope of the line that passes through (–2, –3) and (4, 6) is. 3 2 = y 2 – y 1 x 2 – x 1 3 2 =

7. Slope of a Line 12-2 Find the slope of the line that passes through (–4, –6) and (2, 3). Check It Out: Example 2 Let (x 1, y 1 ) be (–4, –6) and (x 2, y 2 ) be (2, 3). 3 – (–6) 2 – (–4) Substitute 3 for y 2, –6 for y 1, 2 for x 2, and –4 for x 1. 9 6 = The slope of the line that passes through (–4, –6) and (2, 3) is. 3 2 = y 2 – y 1 x 2 – x 1 3 2 =

8. Slope of a Line 12-2 Additional Example 3: 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

9. Slope of a Line 12-2 Additional Example 3 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. = y 2 – y 1 x 2 – x 1 15 5 = 30 – 15 10 – 5 = 3

10. Slope of a Line 12-2 Check It Out: Example 3 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 GallonsCost 00 36 612 6 9 9 6 0 3 3 x y Gallons Cost of Gas Cost

11. Slope of a Line 12-2 Check It Out: Example 3 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. = y 2 – y 1 x 2 – x 1 6 3 = 12 – 6 6 – 3 = 2

12. Slope of a Line 12-2

13. Slope of a Line 12-2

14. Slope of a Line 12-2 Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

15. Slope of a Line 12-2 Lesson Quiz: Part I Find the slope of the line passing through each pair of points. 1. (4, 3) and (–1, 1) 2. (–1, 5) and (4, 2) 2 55 3 –

16. Slope of a Line 12-2 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 64 2 8 101214 0 10 20 30 40 50 60 70 80 The slope of the line is 7. This means Susan earned $7 for each hour worked.

17. Slope of a Line 12-2 1. Identify the slope of the line passing through the pair of points (5, 2) and (–2, 1). A. 7 B. –3 C. D. Lesson Quiz for Student Response Systems

18. Slope of a Line 12-2 2. The table shows the number of hours a student works and her earnings. Identify the slope of the line and explain what it shows. A. The slope of the line is 15. This means that the student earns $15 for every hour that she works. B. The slope of the line is 30. This means that the student earns $30 for every hour that she works. Lesson Quiz for Student Response Systems