Interpreting Rate of Change and Initial Value

Question

You have the choice of starting two jobs for which you have received offers and different salary structures.

 

Offer A: earn $22/hour, but initiallly you will be charged $132 (for your uniform and supplies).

Offer B: earn $16/hour, plus a signing bonus of $600 (for you to address childcare and relocation expenses if you so choose).

 

1. Create a linear function to model the relationship between the number of hours worked and the total income earned in dollars. Let x represent the number of hours worked and y represent the total income earned in dollars. Write a linear equation to represent each job offer.

2. Determine the pay earned from working 20 hours at each job.

3. Graph the equation of the line for both the first offer (Offer A) and the second offer (Offer B) by marking the two points from your work above (for 0 and 10 hours) and drawing a line through these two points.

4. Which line has a steeper slope? Which job's pay structure has the highest rate of hourly pay?

5. Which function has the greater initial value?

6. Which job would you choose if you only wanted to work 60 hours? Which company would you choose if you wanted to work 200 hours? Explain your reasoning.

Answer 1

Nicole,

 

1.  y1=22x-132; y2=16x+600

 

2.  y1(20)=22(20)-132=$308; y2=16(20)+600=$920

 

3.  I must leave that to you.

 

4.  m1=$22/hour>m2=$16/hour.  The rate of hourly pay is the same as the slope of the line.  Job 1's slope is greater.

 

5.  The initial values occur with no work done y1(0)=-132; y2(0)=600  Job 2 has a bonus rather than a charge so its initial value is grater.

 

6. y1(60)=1320-132=1188  y2(60)=960+600=1460. I would prefer job 2 on working 60 hours since my income is greater.

    y1(200)=4400-132=4268  y2(200)=3200+600=3800.  If I were to work200 hours, I would prefer job 1 since 4268>3800