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 + 2no 2.y = 2xyes 3.3x – y = 0yes 4.9x + 3y = -3no 5.2x + 3y = 0yes 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. Is this a direct variation? If so, write the equation. x y 5 9 6 10.8 7 12.6 8 14.4 9 16.2 x y 3 9.1 5 11.1 9 15.1 13 19.1

12. Answers x y 5 9 6 10.8 7 12.6 8 14.4 9 16.2 x y 3 9.1 5 11.1 9 15.1 13 19.1 Yes; y = 1.8xNo

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 2. 3x = 4y – 7 no Tell whether each relationship is a direct variation. Explain. 3.4.

17. 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. 2 4 6