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Lesson 2 Contents Example 1Slope and Constant of Variation Example 2Direct Variation with k > 0 Example 3Direct Variation with k < 0 Example 4Write and

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Page 1: Lesson 2 Contents Example 1Slope and Constant of Variation Example 2Direct Variation with k > 0 Example 3Direct Variation with k < 0 Example 4Write and
Page 2: Lesson 2 Contents Example 1Slope and Constant of Variation Example 2Direct Variation with k > 0 Example 3Direct Variation with k < 0 Example 4Write and

Example 1 Slope and Constant of Variation

Example 2 Direct Variation with k > 0

Example 3 Direct Variation with k < 0

Example 4Write and Solve a Direct Variation Equation

Example 5 Direct Variation Equation

Page 3: Lesson 2 Contents Example 1Slope and Constant of Variation Example 2Direct Variation with k > 0 Example 3Direct Variation with k < 0 Example 4Write and

Name the constant ofvariation for the equation.Then find the slope of theline that passes through thepair of points.

Slope formula

Simplify.

Answer: The constant of variation is 2. The slope is 2.

Page 4: Lesson 2 Contents Example 1Slope and Constant of Variation Example 2Direct Variation with k > 0 Example 3Direct Variation with k < 0 Example 4Write and

Name the constant ofvariation for the equation.Then find the slope of theline that passes through thepair of points.

Slope formula

Simplify.

Answer: The constant of variation is –4. The slope is –4.

Page 5: Lesson 2 Contents Example 1Slope and Constant of Variation Example 2Direct Variation with k > 0 Example 3Direct Variation with k < 0 Example 4Write and

Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points.

a. Answer: constant ofvariation: 4; slope: 4

Page 6: Lesson 2 Contents Example 1Slope and Constant of Variation Example 2Direct Variation with k > 0 Example 3Direct Variation with k < 0 Example 4Write and

Answer: constant ofvariation: –3; slope: –3

Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points.

b.

Page 7: Lesson 2 Contents Example 1Slope and Constant of Variation Example 2Direct Variation with k > 0 Example 3Direct Variation with k < 0 Example 4Write and

Step 1 Write the slope as a ratio.

Step 2 Graph (0, 0).

Step 3 From the point (0, 0), move up 1 unit and right 1 unit. Draw a dot.

Step 4 Draw a line containing the points.

Page 8: Lesson 2 Contents Example 1Slope and Constant of Variation Example 2Direct Variation with k > 0 Example 3Direct Variation with k < 0 Example 4Write and

Answer:

Page 9: Lesson 2 Contents Example 1Slope and Constant of Variation Example 2Direct Variation with k > 0 Example 3Direct Variation with k < 0 Example 4Write and

Step 1 Write the slope as a ratio.

Step 2 Graph (0, 0).

Step 3 From the point (0, 0), move down 3 units andright 2 units. Draw a dot.

Step 4 Draw a line containing the points.

Page 10: Lesson 2 Contents Example 1Slope and Constant of Variation Example 2Direct Variation with k > 0 Example 3Direct Variation with k < 0 Example 4Write and

Answer:

Page 11: Lesson 2 Contents Example 1Slope and Constant of Variation Example 2Direct Variation with k > 0 Example 3Direct Variation with k < 0 Example 4Write and

Suppose y varies directly as x, and when

Write a direct variation equation that relates x and y.

Find the value of k.

Direct variation formula

Replace y with 9 and x with –3.

Divide each side by –3.

Page 12: Lesson 2 Contents Example 1Slope and Constant of Variation Example 2Direct Variation with k > 0 Example 3Direct Variation with k < 0 Example 4Write and

Simplify.

Answer: Therefore,

Page 13: Lesson 2 Contents Example 1Slope and Constant of Variation Example 2Direct Variation with k > 0 Example 3Direct Variation with k < 0 Example 4Write and

Use the direct variation equation to find x when

Direct variation equation

Answer: Therefore, when

Replace y with 15.

Divide each side by –3.

Simplify.

Page 14: Lesson 2 Contents Example 1Slope and Constant of Variation Example 2Direct Variation with k > 0 Example 3Direct Variation with k < 0 Example 4Write and

Suppose y varies directly as x, and when

a. Write a direct variation equation that relates x and y.

b. Use the direct variation equation to find x when

Answer: –15

Answer:

Page 15: Lesson 2 Contents Example 1Slope and Constant of Variation Example 2Direct Variation with k > 0 Example 3Direct Variation with k < 0 Example 4Write and

Travel The Ramirez family is driving cross-country on vacation. They drive 330 miles in 5.5 hours.

Write a direct variation equation to find the distance driven for any number of hours.

Words The distance traveled is 330 miles, and the time is 5.5 hours.

Variables

Distance equals rate times time.

Equation 330 mi r 5.5h

Page 16: Lesson 2 Contents Example 1Slope and Constant of Variation Example 2Direct Variation with k > 0 Example 3Direct Variation with k < 0 Example 4Write and

Solve for the rate.

Answer: Therefore, the direct variation equation is

Original equation

Divide each side by 5.5.

Simplify.

Page 17: Lesson 2 Contents Example 1Slope and Constant of Variation Example 2Direct Variation with k > 0 Example 3Direct Variation with k < 0 Example 4Write and

Graph the equation.

The graph of passes through the origin with a slope of 60.

Answer:

Page 18: Lesson 2 Contents Example 1Slope and Constant of Variation Example 2Direct Variation with k > 0 Example 3Direct Variation with k < 0 Example 4Write and

Estimate how many hours it would take to drive 600 miles.

Original equation

Replace d with 600.

Divide each side by 60.

Simplify.

Answer: At this rate, it will take 10 hours to drive 600 miles.

Page 19: Lesson 2 Contents Example 1Slope and Constant of Variation Example 2Direct Variation with k > 0 Example 3Direct Variation with k < 0 Example 4Write and

Dustin ran a 26-mile marathon in 3.25 hours.

a. Write a direct variation equation to find the distanceran for any number of hours.

b. Graph the equation.

Answer:

Answer:

Page 20: Lesson 2 Contents Example 1Slope and Constant of Variation Example 2Direct Variation with k > 0 Example 3Direct Variation with k < 0 Example 4Write and

c. Estimate how many hours it would take to jog 16 miles.

Answer: 2 hours


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