splash screen. then/now you found rates of change of linear functions. write and graph direct...
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You found rates of change of linear functions.
• Write and graph direct variation equations.
• Solve problems involving direct variation.
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Direct Variation Graphs
• Direct variation equations are of the formy = kx, where k ≠ 0
• The graph of y = kx always passes through the origin
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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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Slope and Constant of Variation
B. Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points.
Answer: The constant of variation is –4. The slope is –4.
(x1, y1) = (0, 0)
(x2, y2) = (1, –4)
Slope formula
Simplify.
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A. Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points.
29%
0%0%
71%
A. constant of variation: 4; slope: –4
B. constant of variation: 4; slope: 4
C. constant of variation: –4; slope: –4
D. constant of variation: slope:
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B. Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points.
0%
93%
7%0%
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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Step 2 Graph (0, 0).
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.
Graph a Direct Variation
Step 1 Find the slope.
m
Answer:
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Graph y = 2x.
0% 4%14%
82%A. B.
C. D. D.
D.
E.
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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.y = kx Direct variation formula
9 = k(–3) Replace y with 9 and x with –3.
Divide each side by –3.
–3 = k Simplify.Answer: Therefore, the direct variation equation is
y = –3x.
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Answer: Therefore, x = –5 when y = 15.
B. Use the direct variation equation to find x when y = 15.
Simplify.
Direct variation equation
Replace y with 15.
Divide each side by –3.
Write and Solve a Direct Variation Equation
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A. Suppose y varies directly as x, and y = 15 when x = 5. Write a direct variation equation that relates x and y. 96%
0%4%0%
A. y = 3x
B. y = 15x
C. y = 5x
D. y = 45x
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B. Suppose y varies directly as x, and y = 15 when x = 5. Use the direct variation equation to find x wheny = –45.
7% 4%
71%
18%
A. –3
B. 9
C. –15
D. –5
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• Assignment– Page 185– Problems 11 – 27, odds
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Estimate Using Direct Variation
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.
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Estimate Using Direct Variation
Solve for the rate.
Answer: Therefore, the direct variation equation is d = 60t.
Simplify.
Original equation
Divide each side by 5.5.
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Estimate Using Direct Variation
B. Graph the equation.
The graph of d = 60t passes through the origin with a slope of 60. Answer:
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Estimate Using Direct Variation
C. Estimate how many hours it would take to drive 500 miles.
Answer: At this rate, it will take about 8.3 hours to drive 500 miles.
Simplify.
Replace d with 500.
Divide each side by 60.
Original equation
8.33 ≈ t
500 = 60t
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A. Dustin ran a 26-mile marathon in 3.25 hours. Write a direct variation equation to find the distance run for any number of hours.
8%0%
8%
83%
A. d = h
B. d = 8h
C. d = 8
D.
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B. Dustin ran a 26-mile marathon in 3.25 hours. Graph the equation.
27%
9%
55%
9%
A. B.
B.
C. D.
D.
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C. Estimate how many hours it would take to jog 16 miles.
0%
91%
0%9%
A. 1 hour
B.
C. 16 hours
D. 2 hours
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