1. Warm UpOct. 15  For numbers 1-3, find the slope of the line that passes through each pair of points 1. (-4, -1) and (-3, -3) 2. (-2, 3) and (8, 3) 3. (0.75, 1) and (0.75, -1) 4. Find the value of r so the line that passes through each pair of points has the given slope. (4, -5) and (3, r), m = 8 5. In 1995, there were 12,458 fish in Hound’s Tooth Lake. After years of drought, there were only 968 fish in 2000. Find the rate of change in the population of fish for 1995–2000.

2. SAT Practice Question

3. Homework Answers

4. Direct Variation (aka slope)  So far we have several names for slope: 1. m 2. linear change 3. rate of change 4. constant of variation  A direct variation is described by an equation of the form y = kx, where k ≠ 0.  In the equation y = kx, k is the constant of variation.

6. Examples:  Write a direct variation equation that relates x and y. Assume y varies directly as x. Then solve. 1. If y = - 8 when x = -2, find y when x = 12. comma splits problem

7. Examples (cont.)  Write a direct variation equation that relates x and y. Assume y varies directly as x. Then solve. 2. If y = 28 when x = 4, find x when y = 56. Answer: Equation: _____ x = ______

8. Graphing y = kx  Start at the origin!  k is your slope = rise = + -_ run + -  Graph: (slope says up 3 and right 2)

9. Examples (cont.)  Graph:  Graph: y = -4x

10.  Graph y = -2/3x

11. Real World Examples  d = rt  distance = rate x time 1. A family drove their car 225 miles in 5 hours. a. Write a direct variation equation to find the distance traveled for any number of hours.  b. Graph the equation.  c. Estimate how many hours it would take the family to drive 360 miles.

12. Examples (cont.)

13. You Try!  Worksheet with Partner

14. You Try! Answers 1. 29. 11. 2. 4 3. -1 4. 3/2 5. y = 2x; 10 6. y = 6x; 710. 12. 7. y = 12x; 1 8. y = 5x; 100

15. Homework Workbook p. 143 # 7 – 17