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5-2 Direct Variation

5-2 Direct Variation. Objective: To write and graph an equation of a direct variation. 5-2 Direct Variation. Start with Getting ready on Page 301. What general rule models this situation. 5-2 Direct Variation. The time it takes to hear thunder directly with the distance from lighting.

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5-2 Direct Variation

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  1. 5-2 Direct Variation Objective: To write and graph an equation of a direct variation

  2. 5-2 Direct Variation • Start with Getting ready on Page 301. • What general rule models this situation.

  3. 5-2 Direct Variation • The time it takes to hear thunder directly with the distance from lighting. • If the ratio of two variables is constant, the variables’ relationship is a direct variation.

  4. 5-2 Direct Variation • A direct variation is represented by a function in the form y = kx, where k  0. k represents the constant of variation. It is the coefficient of x. Can anyone solve the formula y = kx for k?

  5. 5-2 Direct Variation • To determine if an equation represents a direct variation, solve the equation for y. If the form is y = kx, where k is not zero, then it is a direct variation.

  6. 5-2 Direct Variation • Example 1:Direct variations? If YES find k. • A. 7y = 2x B. 3y + 4x = 8 4x + 5y = 0 k?

  7. 5-2 Direct Variation • To write an equation for a direct variation: • Find constant of variation, k, by using an ordered pair (NOT (0,0)) from the information given. • Write equation replacing k with value calculated. y = kx is the equation. • Now that an equation is written, any value of y can be find when given x.

  8. 5-2 Direct Variation • Suppose y varies directly with x, and y = 35 when x = 5. What direct variation equation relates x and y. What is value of y when x = 9?

  9. 5-2 Direct Variation • Suppose y varies directly with x, and y = 10 when x = -2. What equation relates x and y/ What is the value of y when x = -15

  10. 5-2 Direct Variation • Example 3:Weight on Mars y varies directly with weight on Earth x. The weights of the instruments are shown on page 302. • Find an equation using information. • Make a table of values and draw the graph.

  11. 5-2 Direct Variation • Graphs of Direct Variations always look the same. The line passes through (0, 0). The slope is k. What if k is positive? Negative?

  12. 5-2 Direct Variation • Example 4: Look at data in table, does y vary directly with x. YES write an equation. • A. B. • Find y/x for each pair. Does it Change?

  13. 5-2 Direct Variation • HW p. 304 9 – 33 every third

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