1. 5.3.1 Direct Variation

2. Function A direct variation is a function that can be written as A direct variation is a function that can be written as y=kx where k ≠ 0 y=kx where k ≠ 0 k is called the constant of variation k is called the constant of variation Another name for this function is a linear equation Another name for this function is a linear equation

3. slope The constant of variation (k) is also known as a slope The constant of variation (k) is also known as a slope If y=kx then we can divide by x (for x≠0) If y=kx then we can divide by x (for x≠0) k = y/x k = y/x So we can think of k as  y/  x So we can think of k as  y/  x

4. graph Examples: Examples: Note the y-intercepts Note the y-intercepts Non-examples Non-examples Note the y-intercepts Note the y-intercepts y x y x

5. algebraically Non-example Non-example 2x + 10y = 5  2x + 10y = 5  10y = -2x + 5  10y = -2x + 5  y = (-1/5)x + ½ y = (-1/5)x + ½ This equation is not in the form y=kx This equation is not in the form y=kx Example Example 3x + 6y = 0  3x + 6y = 0  6y = -3x  6y = -3x  y = (-½) x y = (-½) x This equation is in the form of y=kx This equation is in the form of y=kx

6. Substitute (0,0) Look back at the two previous equations Look back at the two previous equations 2x + 10y = 5 2x + 10y = 5 3x + 6y = 0 3x + 6y = 0 Substitute (0,0) does the equation make sense? Substitute (0,0) does the equation make sense?

7. Real world situation: Working in retail: Working in retail: As a retail associate a person makes an hourly wage, for example As a retail associate a person makes an hourly wage, for example You worked 40 in a week and your pay check (before taxes) is $300 You worked 40 in a week and your pay check (before taxes) is $300 The amount you are paid varies directly as the amount of hours you work ($/hr) The amount you are paid varies directly as the amount of hours you work ($/hr) k = $300/40hrs = $7.50/1hour (average rate of change) k = $300/40hrs = $7.50/1hour (average rate of change) y = 7.50x y = 7.50x

8. Does x vary directly as y X Y -2 1 3 6 8 11 X Y -2 1 3 -6 8 -16 Find k for all 3 points in both situations Find k for all 3 points in both situations

9. Homework: P. 228 1-19 odd, 22, 23, 25 P. 228 1-19 odd, 22, 23, 25