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Direct Variation

Direct Variation. A direct variation is…. A linear equation The y-intercept must be zero!!!! The graph of a direct variation will ALWAYS go through the origin (0,0). In the equation, there will only be numbers with the variables (coefficients). The only other number used can be zero.

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Direct Variation

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  1. Direct Variation

  2. A direct variation is… • A linear equation • The y-intercept must be zero!!!! • The graph of a direct variation will ALWAYS go through the origin (0,0). • In the equation, there will only be numbers with the variables (coefficients). The only other number used can be zero.

  3. This is a direct variation…

  4. Which is a direct variation? • 1. y = 3x + 2 • 2. y = 2x • 3. 3x – y = 0 • 4. 9x + 3y = -3 • 5. 2x + 3y = 0 • 6.

  5. Which is a direct variation?-Answers • 1. y = 3x + 2 no • 2. y = 2x yes • 3. 3x – y = 0 yes • 4. 9x + 3y = -3 no • 5. 2x + 3y = 0 yes • 6. yes

  6. Constant of Variation • The constant of variation is the rate of change for the data that describes the variation (slope) • The constant of variation is found by dividing “y” by “x” • It is the slope of a linear equation whose y-intercept is zero!!!! • “They” call it “k”. Y = kx

  7. Equation of a Direct Variation y = kx

  8. Suppose the ordered pair in each problem are for a direct variation. Write the equation of direct variation.

  9. 1. (2, 1) • 2. (15, 12) • 3. (6, 4) • 4. (1.4, 2.8) • 5.

  10. Answers • 1. (2, 1) y = 1/2x • 2. (15, 12) y = 4/5x • 3. (6, 4) y = 2/3x • 4. (1.4, 2.8) y = 2x • 5. y = -2x

  11. x y • 9 • 10.8 • 12.6 • 14.4 • 16.2 • x y • 3 9.1 • 11.1 • 15.1 • 13 19.1 Is this a direct variation? If so, write the equation.

  12. x y • 9 • 10.8 • 12.6 • 14.4 • 16.2 • x y • 3 9.1 • 11.1 • 15.1 • 13 19.1 Answers Yes; y = 1.8x No

  13. Write a direct variation for the following…

  14. Example 1 • The distance that you travel at a constant speed varies directly with the time spent traveling. It takes you 2 hours to travel 100 miles. • Write an equation for the relationship between the time and distance. • How far can you travel in 3.5 hours? • How long will it take you to travel 400 miles?

  15. Example 2 • The money you earn varies directly with the number of lawns you mow. You earn $36 for mowing 3 lawns. • Write an equation for the relationship between money earned and lawns mowed. • How much money would you earn for mowing seven lawns? • How many lawns did you mow for $60?

  16. Try these… Tell whether each equation represents a direct variation. If so, identify the constant of variation. 1.2y = 6x yes; 3 no 2.3x = 4y – 7 Tell whether each relationship is a direct variation. Explain. 3. 4.

  17. 6 4 2 Try These… Part II 5. The value of y varies directly with x, and y = –8 when x = 20. Find y when x = –4. 1.6 6. Apples cost $0.80 per pound. The equation y = 0.8x describes the cost y of x pounds of apples. Graph this direct variation.

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