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Math Pacing

Slope and Direct Variation. Math Pacing. Slope and Direct Variation. A direct variation is described by an equation of the form y = kx , where k ≠ 0 We say that y varies directly with x or y varies directly as x . In the equation, y = kx , k is the constant of variation.

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Math Pacing

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  1. Slope and Direct Variation Math Pacing

  2. Slope and Direct Variation A direct variation is described by an equation of the form y = kx, where k≠ 0 We say that y varies directly with x or y varies directly as x. In the equation, y = kx, kis the constant of variation. Slope and Direct Variation

  3. Slope formula Simplify. Slope and Constant of Variation Example 2-1a Name the constant ofvariation for the equation.Then find the slope of theline that passes through thepair of points. The constant of variation is 2. Answer: k = 2 and m = 2. Notice that the slope of the graph of y = kx is k. For a direct variation, the slope and constant of variation are identical.

  4. Slope formula Simplify. Slope and Constant of Variation Example 2-1b The constant of variation is – 4. Name the constant ofvariation for the equation.Then find the slope of theline that passes through thepair of points. Answer: k = – 4 and m = – 4. The ordered pair (0, 0) is a solution of y = kx. Therefore, the graph of y = kx passes through the origin. You can use this information to graph direct variation equations.

  5. Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points. a. Slope and Constant of Variation Example 2-1c Answer: constant of variation: 4; slope: 4

  6. b. Slope and Constant of Variation Example 2-1d Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points. Answer: constant of variation: –3; slope: –3 The ordered pair (0, 0) is a solution of y = kx. Therefore, the graph of y = kx passes through the origin. You can use this information to graph direct variation equations.

  7. Direct Variation with k > 0 Example 2-2a Step 1Write the slope as a ratio. Step 2Graph (0, 0). Step 3From the point (0, 0), move up 1 unit and right 1 unit. Draw a dot. Step 4Draw a line containing the points.

  8. Answer: Direct Variation with k > 0 Example 2-2b

  9. Direct Variation with k < 0 Example 2-3a Step 1Write the slope as a ratio. Step 2Graph (0, 0). Step 3From the point (0, 0), move down 3 units andright 2 units. Draw a dot. Step 4Draw a line containing the points.

  10. Answer: Direct Variation with k < 0 Example 2-3b

  11. Slope and Direct Variation k is the constant of variation Slope and Direct Variation Copy this in your notes, please!

  12. Suppose y varies directly as x, and when • Write a direct variation equation that relates x and y. Simplify. Answer: Therefore, Direct variation formula Replace y with 9 and x with –3. Divide each side by –3. Write and Solve a Direct Variation Equation Example 2-4a Find the value of k.

  13. Use the direct variation equation to find x when Direct variation equation Replace y with 15. Divide each side by –3. Simplify. Answer: Therefore, when Write and Solve a Direct Variation Equation Example 2-4c

  14. 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: Example 2-4d Write and Solve a Direct Variation Equation Answer: x =–15 Write this in your notes:

  15. Variables 330 mi r 5.5h Equation Direct Variation Equation Example 2-5a 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. Distance equals rate times time.

  16. Original equation Divide each side by 5.5. Simplify. Answer: Therefore, the direct variation equation is Direct Variation Equation Example 2-5b Solve for the rate. Write this in your notes:

  17. The graph of passes through the origin with a slope of 60. Answer: Direct Variation Equation Example 2-5c Graph the equation.

  18. Original equation Replace d with 600. Divide each side by 60. Simplify. Direct Variation Equation Example 2-5d Estimate how many hours it would take to drive 600 miles. Answer: At this rate, it will take 10 hours to drive 600 miles.

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