Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

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

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

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

Vocabulary rise run slope 5

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

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. slope = = 2 4 1 The slope of the line is . 1 2

Find the slope of the line. 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) slope = = 1 4 The slope of the line is 1.

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: y2 – y1 x2 – x1 m =

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

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. Pounds Cost Cost of Fruit Graph the data.

Additional Example 3 Continued Find the slope of the line: = y2 – y1 x2 – x1 30 – 15 10 – 5 15 5 = = 3 The slope of the line is 3. This means that for every pound of fruit, you will pay another $3.

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

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

Lesson Quiz for Student Response Systems Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 18 18

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 5 5 3 –

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

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. 21 21

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. 22 22