Interpreting Situations as Functions

A lawn mowing service charges a 10 flat rate, plus7 per hour. Write an equation for the cost of a job as a function of the hours it takes. If a particular lawn costs $38 to mow, how many hours did it take?

  • cost=c
  • hours=h

h=0,\ c=10,\ (0,\ 10)

h=1,\ c=17,\ (1,\ 17)


b=10,\ (0,\ 10)

y=mx+b\rightarrow y=7x+b\rightarrow y=7x+10\rightarrow c=7h+10

38=7h+10\rightarrow 38-10=7h+10-10\rightarrow \frac{28}{7}=\frac{7h}{7}\rightarrow 4=h


One number is twice as large as three more than another number. The product of the numbers is 20. What are they?

  1. x=2(y+3)
  2. (x)(y)=20

Substitute eq 1. into eq 2.






factors\ of\ -10:\ [\pm 1,\ \pm 10],\ [\pm 5,\ \pm 2]


y+5=0\rightarrow y=-5

y-2=0\rightarrow y=2

Substitute back into eq 2.

(x)(-5)=20\rightarrow \frac{(x)(-5)}{-5}=\frac{20}{-5}\rightarrow x=4

(x)(2)=20\rightarrow \frac{(x)(2)}{2}=\frac{20}{2}\rightarrow x=10

Two solutions:

  1. x=-4,\ y=-5
  2. x=10,\ y=2