1. A

2. B

3. C

4. D

Determine the slope of the line that passes through the points (–3, 6) and (2, –6).

11/8 Honors Algebra Warm-up

A.

B.

C. 0

D. undefined

HW Questions: pgs. 193-194 #20-38even, 42-50

20. 4/7

22. 1

24. undefined

26. 10/7

28. -2

30. 0

32. -1

34. 1

36. 15/4

38. -2/3

42. s/r if r ≠ 0

43. Undefined

44. 1/4

45. 1/3

46. 12

47. 7

48. See graph below.49. 12-14; steepest part of the graph 50. There was no change in height

during those two years.

Direct Variation – equation of the form:

y =kx where k ≠ 0 •k is the constant of variation.•k = m• x and y are proportional (y/x is the same)

Slope and Constant of Variation

A. Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points.

(x1, y1) = (0, 0)

(x2, y2) = (1, 2)Answer: The constant of variation is 2. The slope is 2.

Slope formula

Simplify.

A. A

B. B

C. C

D. D

B. Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points.

A. constant of variation: 3; slope: 3

B. constant of variation: slope:

C. constant of variation: 0; slope: 0

D. constant of variation: –3; slope: –3

What ordered pair will a direct variation graph always pass through?

Graph a Direct Variation

A. Graph y = x.

Step 1 Plot (0,0).

Step 2 Write slope as ratio.

Step 3 From the point (0, 0), move up 1 unit and right 1 unit. Draw a dot.

Step 4 Draw a line connecting the points.

Graph a Direct Variation

Step 1 Graph (0, 0).

Step 2

Step 3 From the point (0, 0), move down 3 units and right 2 units. Draw a dot.

Step 4 Draw a line connecting the points.

B.

Write the slope as a ratio.

Write and Solve a Direct Variation Equation

A. Suppose y varies directly as x, and y = 9 when x = –3. Write a direct variation equation that relates x and y.Find the value of k.

B. Use the direct variation equation to find x when y = 15.

A. TRAVEL The Ramirez family is driving cross-country on vacation. They drive 330 miles in 5.5 hours. Write a direct variation equation to find the distance driven for any number of hours.

Distance = rate x time.

B. Graph the equation.

The graph of d = 60t passes through the origin with a slope of 60.

Answer:

C. Estimate how many hours it would take to drive 600 miles.

Answer: At this rate, it will take 10 hours to drive 600 miles.

Simplify.

Replace d with 600.

Divide each side by 60.

Original equation