Choose all the relationships that
are described by the following equation-- y is equal to 7/8 x.
All right, let's look at these relationships.
Relationship A-- a bouquet of 8 daisies
cost $7 at Flora's Flowers.
A bouquet of 12 daisies costs $11.
The equation describes the relationship
between the number of daisies, x, and their price
at Flora's Flowers, y.
So let's look at scenario A.
So our x is the number of daisies,
and our y is their price.
So when we get 8 daisies, they say it costs us $7.
When we get 12 daisies, they tell us that it cost $11.
So let's see whether this relationship right over here
is the same as this relationship right over here.
So if I were to take-- so let me write this right over here.
So here, it says y needs to be equal to 7/8 x.
So let's figure out what's 7/8 x is equal to.
So if I take 7/8 times 8-- well, that's going to be 7.
Let me write this down.
7 over 8 times 8 is equal to 7.
So this checks.
7/8 x is the same as the price that they gave us.
So so far, these two seem consistently,
at least based on this first data point.
Now let's look at 7/8 of 12.
Let's see, if we divide 12 and 8 each by 4,
this is going to be the same thing as 7 times 3 over 2,
which is the same thing as 21 over 2, which is equal to 10.5.
So if y were equal to 7/8 x, 12 daisies would cost $10.50.
But we just learned that 12 daisies cost $11.
So these two things aren't equal to each other.
So this is not the same relationship.
In this scenario, y does not equals 7/8x,
so we can rule this one out.
Let's look at relationship B. There's a 12.5% discount
for every item at Crazy Joe's.
The equation describes a relationship
between a given item's price before the discount
and after the discount.
So here, they're giving us a percentage.
And this equation right over here
it's written as a fraction.
So let me at least convert this into a fraction,
and see what kind of a fractional discount this is.
And maybe I can construct an equation,
and see if that equation is the same as this one here.
So 12.5% is the same thing as 12.5 over 100.
And if we multiply the numerator and denominator by 10,
that's the same thing as 125 over 1,000.
Now let's see if we can simplify this a little bit.
If we divide the numerator-- well,
actually, it looks like they're both divisible by 125.
We divide the numerator by 125, we get 1.
We divide the denominator by 125, we get 8.
8 times 125 is 800 plus 200, which is 1,000.
So this is the same thing as 1/8.
So really, there is a 1/8 discount for every item
at Crazy Joe's.
The equation describes a relationship
between a given item's price before the discount
and the price after the discount.
So let's just think about that.
The price after the discount, based
on the information they gave here,
is going to be equal to the price
before the discount minus the discount.
So minus 1/8 of the original price.
Well, what's x minus 1/8 x?
Or another way of thinking about, what's 1x minus 1/8 x?
Well, that's just going to be 7/8 x?
So this relationship is the exact same
as this one over here.
The price after the discount is 7/8 of the original price.
So we can feel good about this one.
These two are the same.
Let's look at scenario C. And I will do scenario C in orange.
A ticket to the paint ball arena cost $7,
and comes with 8 paint balls.
Every extra paint ball costs $1.
The equation describes the relationship
between the number of paint balls x and their price y.
So let's look at this.
We'll do something similar to what we did up here.
So we'll have x, which is the number of paint balls.
And then we have y, which is their price.
And then we will think about what 7/8
x would have been equal to.
And let's see if y is equal to 7/8 x.
So when we get 8 paint balls-- so
x is the number of paint balls.
So when we get 8 paint balls, the price is 7.
And if we take 7/8 x-- so 7/8 times 8 is indeed 7.
So in this scenario, for this data point,
it is true that y is equal to 7 x.
Now let's get a couple of other data points.
And we might have to construct these.
So every extra paint ball costs $1.
So if we have one extra paint ball--
so we have 9 paint balls-- we're going
to have to pay 1 more dollar.
We're going to have to pay $8.
And so, what's 7/8 x here?
So 7/8 times 9?
Well, we don't even have to compute it.
This is going to be something that's going to be like 63/8.
64/8 would be 8.
So this is a little bit less than 8.
But the important point is that 8 is not equal to 63/8.
y does not equal 7/8 x in this scenario right over here.
So this equation does not describe all of these data
points, so we can rule that out
Finally, they say the equation corresponds
to the graph following graph.
So let's see if y equals 7 x corresponds to this graph
right over here.
So what we're really saying is that for any x,
y is going to be 7/8 of that?
And the easiest one is to see when x is equal to 8.
When x is equal to 7/8, x would be 7.
When x is 0, 7/8 of 0 will be 0.
And so, linear relationship-- if we have a line,
and if it goes through the origin,
it is a proportional relationship--
that the ratio between the x and the y-axis
is always going to be the same, or between the y and the x
values is also always going to be the same.
And we know that that ratio is the correct one.
The ratio of y to x throughout this line is 7/8.
Here, it literally is-- our numbers are 7/8.
Well, we can even take other points.
The ratio of 3 and 1/2 to 4 is still the same thing as 7/8.
So this relationship, relationship
D-- the relationship described by the graph--
does coincide with the relationships described
by this equation.
So I would go with B and D.