Math help please

Question

You buy a bottle of water and a dish of frozen yogurt. The table shows the total cost of the purchase for different amounts of frozen yogurt. Write a linear model the represents the total cost as a function of the number of ounces of frozen yogurt.

Ounces of frozen yogurt, x: 4, 4.5, 5, 5.5, 6

Total cost, y: 3.20, 3.35, 3.50, 3.65, 3.80

Answer 1

X (oz) Y (cost)

4 3.20

4.5 3.35

5 3.50

5.5 3.65

6 3.80

We need to solve for Y=mX+b

m is the the slope which is the change in Y over the change in X

The increments of X values are 0.5

The increments of y values are 0.15

Change in Y/Change in X= 0.15/0.5 = 0.3

We now know the slope is 0.3

We have Y=0.3X+b

there are 3 missing variables, we can use one of the points from the table given to solve for b

using point one (4,3.20) X=4 and Y= 3.20

Plugging in, 3.20 = 0.3 (4) + b

b=2

Now you have the general equation:

y = 0.3x + 2

You can double check by plugging in all of the x values and seeing the y values that come out!

Answer 2

For questions like this, it is best to think about it graphically.

Think about what is your dependent and independent variable.

Independent Variable (what you control) : Ounces of froyo

Dependent Variable (what is changed based on what you control) : Total cost

When we graph this, the table then gives us coordinate points to put down. (4,3.20),(4.5,3.35)...

What you have to notice is that both x and y are increasing linearly on the table. What this means is that there is a constant rate that each is increasing. x is increasing in increments of 0.5 ounces and y is increasing in increments of $0.15.

This is where the slope formula comes into play. Rise over run is going to be our change in y over our change in x. So we can definitively say that the cost increases by $0.15 for each 0.5 ounces of frozen yogurt. But we want to write this as a function of x.

In order to do that, we want to write the the equation in the form y=mx+b where m is the slope (we just found this) and b is the y-intercept, in other words what would y be if x were 0.

Once you have a cleaned up version of the slope and you've found the y-intercept, you have your answer!

f(x) = mx + b

Answer 3