Question

Let’s remind ourselves of what “linear” means. A linear function can be expressed in the form: y =mx+b $8AeGLPc73hWkYAAAAASUVORK5CYII=$ . Linear functions do not always have to be in this form, but it is the most common representation. Let’s remind ourselves of what the “pieces” in this expression y =mx+b $8AeGLPc73hWkYAAAAASUVORK5CYII=$ mean.

m is _________

You may have learned this as riserun

           

Remember that rise is a change in _____-values and

                       

run is a change in _____-values

b is the _____-intercept

Graphically, this is _______________________________________________________

and this occurs when x = _______

It may also be helpful to remember that the ______-intercept

graphically is ___________________________________________________________

            and this occurs when y = ________

Hopefully this has reminded you of what a linear function is mathematically. Now, let’s see how these linear functions can help us in some “real world” contexts.

1. Your friends are trying to get an idea of how many people they can invite to their wedding. The venue they’re looking at costs about $2,000 to rent and the event coordinator suggested that they budget about $100 per attendee into the costs.

1. Write a function that represents an estimate for how much this will cost if they have x attendees.

           

2. Now rewrite your function from part (a) with units for each of the values (including the variables).

3. Suppose the venue has a maximum capacity of 250 people. What is an estimated maximum cost for using that venue?

4. Suppose your friends are trying to stick to about $20,000 for their budget. About how many guests can they invite?

Answer 1

it to tal dst 4 rent a000 tost Corst ber ati end ees attende es= number (a) - 100n + d000 e tplonargupap j00 d01lay x n + 200o dollar dol laY (e) 100X25O 2000 2 5o0o 2000 7000 CMacimum Cst 20 000 (d) 100n t2000 20000 l00n 18000 18000 0 g4est