Transcript Direct Variation Equations Review What is the slope? Slope = 1/2

Direct Variation Equations
Review
What is the slope?
Slope = 1/2
Slope = -1
Slope = 5
Slope = Undefined
1. What was the greatest speed that Michael
traveled?
65 mph
2. What does the horizontal segment of the graph
represent? How long does Michael stay at this speed?
Constant Speed
70 mins - 20 mins
= 50 mins
3. What does the segment with a negative slope tell
you about Michael’s speed?
Speed is
decreasing
4. What does the segment with a positive slope tell you
about Michael’s speed?
Speed is
increasing
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 of
variation for the equation.
Then find the slope of the
line that passes through the
pair of points.
Slope formula
Simplify.
Answer: The constant
of variation is 2.
The slope is 2.
Name the constant of
variation for the equation.
Then find the slope of the
line that passes through the
pair 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 of
variation: 4;
slope: 4
Name the constant of variation for the equation.
Then find the slope of the line that passes through
the pair of points.
b.
Answer: constant of
variation: –3;
slope: –3
• The constant of variation is the slope
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
15 = k(5)
Replace y with 15 and x with 5.
15 = k(5)
5
5
Divide each side by 5
3=k
Equation?
y = 3x
Simplify
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
9 = k(3)
9= k(3)
3 3
3=k
Equation?
y = 3x
Replace y with 15 and x with 5.
Divide each side by 5
Simplify
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
18 = k(11)
18= k(11)
11
11
18 = k
11
Equation?
y = 18x
11
Replace y with 15 and x with 5.
Divide each side by 5
Simplify
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
42 = k(7)
Replace y with 15 and x with 5.
42= k(7)
7
7
6=k
Divide each side by 5
Simplify
Equation?
y = 6x
Y varies directly as x. Find the constant of variation
and write an equation for the direct variation.
13. y = 12 when x = 22
Find the value of k.
Direct variation formula
12 = k(22)
Replace y with 15 and x with 5.
12= k(22)
22
22
6=k
11
Equation?
Divide each side by 5
Simplify
y=6x
11
Graph the equation.
The graph of
slope of 60.
Answer:
passes through the origin with a