Talk about Algebra: Make your Own Problems

How often are you told that it's a "Good Thing" to create problems for yourself?

Here's your challenge:  Write a story problem following the model shown below.  Then compute the slope for that set of data and, of course, show your work.  You have to have at least 4 data points (and thus 3 slopes to calculate and compare).

You may even find one of your problems snuck onto Monday's Quiz, which while your classmates may dislike, you at least will know the answer!

Here's a sample with solution:

A local indoor play center can be rented for kid's birthday parties.  With Xander rapidly approaching the ripe ol' age of 3, we decide to investigate one.  Asking some people who've been to Jungle Jim's Jamboree, we find that they've had parties there too and here is the data we got:
10 kids, $70
12 kids, $82
15 kids, $100
20 kids, $130

Does this follow a linear relationship?  What's the slope?

Now on to the solution:


Since this is text please excuse the notation to create the fractions for slope.

Remember that the slope formula is:  (Y2 - Y1) / (X2 - X1)

So over the first interval:  (82 - 70) / (12 - 10) = 12 / 2 = $6 / kid.
Second:  (100 - 82) / (15 - 12) = 18 / 3 = $6 / kid
Third:  (130 - 100) / (20 - 15) = 30 / 5 = $6 / kid

Since the slope is the same at $6 / kid, this ~is~ a linear relationship.

So for 3 Brownie Points, write your own problem like this.  Think of two things that might be related linearly and create a table of 4 values that represent it.  Now, to be fair, I came up with my slope first and generated my points from that slope.

If you're still not sure how this all works you may want to review the class videos on computing slope and on linear relationships.