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Warm Up

Warm Up. Problem of the Day. Lesson Presentation. Lesson Quizzes. Warm Up Evaluate each equation for x = –1, 0, and 1. 1. y = 3 x 2. y = x – 7 3. y = 2 x + 5 4. y = 6 x – 2. –3, 0, 3. –8, –7, –6. 3, 5, 7. –8, –2, 4. Problem of the Day

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Warm Up

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  1. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

  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. Problem of the Day Write a linear equation that contains terms with x2. Possible answer: x2 + y = x2 + x + 4

  4. Learn to find the slope of a line and use slope to understand and draw graphs.

  5. Vocabulary rise run slope

  6. The constant rate of change of a line is called the slope of the line.

  7. 2 4 1 2 1 2 slope = = The slope of the line is . Additional Example 1: Finding the Slope of a Line Find the slope of the line. (5, 4) Begin at one point and count vertically to find the rise. (1, 2) Then count horizontally to the second point to find the run.

  8. 4 4 slope = = 1 The slope of the line is 1. Check It Out: Example 1 Find the slope of the line. Begin at one point and count vertically to find the rise. (3, 2) Then count horizontally to the second point to find the run. (–1, –2)

  9. y2–y1 x2–x1 m = 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 (x1, y1) and (x2, y2) is as follows:

  10. y2 – y1 = x2 – x1 6 – (–3) 3 9 4 – (–2) 3 The slope of the line that passes through (–2, –3) and (4, 6) is . 6 2 2 = = Additional Example 2: Finding Slope, Given Two Points Find the slope of the line that passes through (–2, –3) and (4, 6). Let (x1, y1) be (–2, –3) and (x2, y2) be (4, 6). Substitute 6 for y2, –3 for y1, 4 for x2, and –2 for x1.

  11. y2 – y1 = x2 – x1 3 – (–6) 3 9 2 – (–4) 3 The slope of the line that passes through (–4, –6) and (2, 3) is . 6 2 2 = = Check It Out: Example 2 Find the slope of the line that passes through (–4, –6) and (2, 3). Let (x1, y1) be (–4, –6) and (x2, y2) be (2, 3). Substitute 3 for y2, –6 for y1, 2 for x2, and –4 for x1.

  12. Cost of Fruit Cost Pounds 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.

  13. y2 – y1 = x2 – x1 30 – 15 15 10 – 5 5 = = 3 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.

  14. y Cost of Gas 12 9 Cost 6 3 9 0 3 6 x Gallons 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.

  15. y2 – y1 = x2 – x1 12 – 6 6 6 – 3 3 The slope of the line is 2. This means that for every gallon of gas, you will pay another $2. = = 2 Check It Out: Example 3 Continued Find the slope of the line:

  16. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

  17. 2 5 3 – 5 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)

  18. y 80 70 60 50 40 The slope of the line is 7. This means Susan earned $7 for each hour worked. 30 20 10 x 0 2 10 12 14 4 6 8 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.

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

  20. Lesson Quiz for Student Response Systems 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.

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