direct variation equations. review what is the slope?
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Direct Variation Equations
ReviewWhat is the slope?
Slope = 1/2
Slope = -1
Slope = 5
Slope = Undefined
65 mph
1. What was the greatest speed that Michael traveled?
Constant Speed
2. What does the horizontal segment of the graph represent? How long does Michael stay at this speed?
70 mins - 20 mins = 50 mins
Speed is decreasing
3. What does the segment with a negative slope tell you about Michael’s speed?
Speed is increasing
4. What does the segment with a positive slope tell you about Michael’s speed?
Vocabulary
• Direct Variation Equation – An equation of the form y = kx, where k does not equal zero
• Constant of Variation – k in a direct variation equation
Name the constant ofvariation for the equation.Then find the slope of theline that passes through thepair of points.
Slope formula
Simplify.
Answer: The constant of variation is 2. The slope is 2.
Name the constant ofvariation for the equation.Then find the slope of theline that passes through thepair of points.
Slope formula
Simplify.
Answer: The constant of variation is –4. The slope is –4.
Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points.
a. Answer: constant ofvariation: 4; slope: 4
Answer: constant ofvariation: –3; slope: –3
Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points.
b.
• The constant of variation is the slope
Find the value of k.Direct variation formula
15 = k(5) Replace y with 15 and x with 5.
15 = k(5) 5 5 Divide each side by 5
3 = k Simplify
Equation?
y = 3x
Y varies directly as x. Find the constant of variation and write an equation for the direct variation.5. Y = 15 when x = 5
Find the value of k.Direct variation formula
9 = k(3) Replace y with 15 and x with 5.
9= k(3)3 3 Divide each side by 5
3 = k Simplify
Equation?
y = 3x
Y varies directly as x. Find the constant of variation and write an equation for the direct variation.7. Y = 9 when x = 3
Find the value of k.Direct variation formula
18 = k(11) Replace y with 15 and x with 5.
18= k(11)11 11 Divide each side by 518 = k Simplify11
Equation?
y = 18x 11
Y varies directly as x. Find the constant of variation and write an equation for the direct variation.9. y = 18 when x = 11
Find the value of k.Direct variation formula
42 = k(7) Replace y with 15 and x with 5.
42= k(7) 7 7 Divide each side by 56 = k Simplify
Equation?
y = 6x
Y varies directly as x. Find the constant of variation and write an equation for the direct variation.11. y = 42 when x = 7
Find the value of k.Direct variation formula
12 = k(22) Replace y with 15 and x with 5.
12= k(22)22 22 Divide each side by 56 = k Simplify11
Equation?
y = 6 x 11
Y varies directly as x. Find the constant of variation and write an equation for the direct variation.13. y = 12 when x = 22
Graph the equation.
The graph of passes through the origin with a slope of 60.
Answer:
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