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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
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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.
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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)
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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.
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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
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What ordered pair will a direct variation graph always pass through?
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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.
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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.
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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.
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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.
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B. Graph the equation.
The graph of d = 60t passes through the origin with a slope of 60.
Answer:
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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