You have just started your first job at the local ice cream
shop making minimum wage. (Ohio's minimum wage is $8.30
per hour.) Complete the table and graph below to reflect your earnings.
What does x represent?
x
1
2
What does y represent?
3
4
7
10
y
Because you are
such a wonderful
worker after the
first month you
are given a $2/
hour raise.
How does this raise effect the table?
How does this raise affect the graph?
x
y
1
2
3
4
7
10
For each example below, decide if x and y are in a proportional
relationship. Explain your reasoning.
For the proportional relationships above,
- State the slope
- Find the value of y for the ordered pair (1, y)
- What do you notice? What does the value of y represent?
For the proportional
relationships above,
1.2 Let's be
Direct . . .
Direct
direct variation - a relationship . . .
a proportional relationship,
where y/x always equals the same number
the line always crosses thru the origin
We can tell a relationship is a direct variation if the table . . .
the quotient of y divided by x is always the
same AND y = 0 when x = 0
We can tell a relationship is a direct variation if the graph . . .
is a line that goes through the origin
We can tell a relationship is a direct variation if the equation . . .
can be written in the form y = mx
ie: no exponents, can't divide by x or y, can't
multiply x and y together AND
there is not a constant (ie no # without a variable)
Recap:
Looking at the table/graph for the situations we
discussed yesterday, how can we tell each
represents a proportional relationship?
Direct Variation or Not?
3
6
8
11
14
17
20
Direct Variation or Not?
2x - 5y = 12
7y = -2x
2xy = 12
x = 1/2 y
2x = 6
y
-3x + y = 11
5
y=x
3 5
x3 - 2y = -4
2.
3.
4.
Pull
y = 3x
4
1.
Pull
y = 2x - 5
Pull
y = mx
y = 4x
Not a
Direct
Variation
Pull
Direct
Variation
No variables have
exponents larger than 1.
x and y cannot be multiplied
or divided together
x and y must be in the
numerator
NO constants
ie. BP = 0
Are these direct variations or not?
direct variation
y = 25 x
5y = 8x
y = 9x
not
y = -3x - 4
6x = 2y - 8
y = 4x2
8 =x
y
2x + 3y = 14
Identify the DIRECT VARIATION shown in each table or graph.
Then, write the relationship in the form y = kx.
Direct Variation:
____ = _____ ______
y = k
Direct Variation:
Direct Variation:
x
____ = _____ ______
y = k
x
____ = _____ ______
y = k
x