functions/graphing: consultant works 10 hrs/day, 6 days/wk

[santaclaus]

A business consultant works 10 hours a day, 6 days a week. She divides her time between meetings with clients and meetings with co-workers. A client meeting requires 3 hours while a co-worker meeting requires 2 hours. Let x be the number of co-worker meetings the consultant holds during a given week. If y is the number of client meetings for which she has time remaining, then y is a function of x. Assume this relationship is linear and that meetings can be split up and continued on different days.

1. how do I go about graphing the relationship between y and x?
2. how do I find a formula for y as a function of x?
3. what does the slope and the x and y-intercepts represent in the context of the consultant's meeting schedule?
4. A change is made so that co-worker meetings take 90 minutes instead of 2 hours. what will the features of this graph that have changed from the one in q 1 and those that have remained the same?

[stapel_eliz]

A business consultant works 10 hours a day, 6 days a week. She divides her time between meetings with clients and meetings with co-workers. A client meeting requires 3 hours while a co-worker meeting requires 2 hours. Let x be the number of co-worker meetings the consultant holds during a given week. If y is the number of client meetings for which she has time remaining, then y is a function of x. Assume this relationship is linear and that meetings can be split up and continued on different days.

1. how do I go about graphing the relationship between y and x?

First, you find the relationship. Then you graph it.

2. how do I find a formula for y as a function of x?

i) How many hours does she work in a week?

ii) How many hours does she use for "x" co-worker meetings? (Hint: This part uses "x".)

iii) How many hours does she have left for client meetings? (Hint: Subtract (ii) from (i).)

iv) Name your formula in (iii) as "y".

Your equation in (iv) is the formula you need.

3. what does the slope and the x and y-intercepts represent in the context of the consultant's meeting schedule?

Use what you learned when you studied the lesson on the meaning of slope and y-intercept in word problems.

4. A change is made so that co-worker meetings take 90 minutes instead of 2 hours. what will the features of this graph that have changed from the one in q 1 and those that have remained the same?

Work through the steps above to create a new model. Graph it on the same set of axes as your first model. Compare the two lines.