CCSS.MATH.CONTENT.8.F.B.4: Construct a function to model a linear relationship between two quantities.
Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y)
values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a
linear function in terms of the situation it models, and in terms of its graph or a table of values.
It’s a question that’s been on the minds of every grocery shopper since the dawn of
civilization: Are the popular name-brand products really worth more than their store-brand
counterparts, or are we simply paying more for the name? People have suspected for
years that the name was the only real difference-maker, but now, thanks to linear
equations, we can find out for sure.
1. Go to a grocery store and select a product. Find two versions of this product: a
popular name brand, and the store brand. Write down the prices for two different sizes of
the name-brand version, then the prices for two different sizes of the store-brand version.
2. Convert the information into ordered pairs, with the x-value being the size of the
product, and the y-value being its price. So the pairs you should have would look like
this:
(size of smaller name-brand item, price of smaller name-brand item)
(size of larger name-brand item, price of larger name-brand item)
(size of smaller store-brand item, price of smaller store-brand item)
(size of larger store-brand item, price of larger store-brand item)
3. Using the two ordered pairs from the name-brand item, figure out the
equation of the line containing them.
4. Repeat step 3 with the ordered pairs from the store-brand item.
5. Compare the two equations. The slope of each line represents the actual cost of the
item per unit, while the y-intercept represents the cost of the packaging. Where was the
bigger difference? What does this tell you about the price of name-brand items vs. the
price of the store-brand counterparts?
6. Graph the two equations on the same xy-plane. Label each line as either the store
brand pricing plan or the name brand pricing plan.