The amount a taxi driver charges a customer is given by the equation `A=1.25+5.25,` where `A` is the total amount charged and `k` is the kilometers driven. a) What do the numbers in the equation...

The amount a taxi driver charges a customer is given by the equation `A=1.25+5.25,` where `A` is the total amount charged and `k` is the kilometers driven.

a) What do the numbers in the equation represent?

b) Make a table of values for distances 0-10 km.

c) Graph this relation. Liner or non-linear?

d) Using your graphed relation, how much is charged if a person goes `7.5` km?

e) Using your graphed relation, how far can a person go in a taxi for \$`15`?

Expert Answers
Borys Shumyatskiy | Certified Educator

Hello! I suppose the equation is `1.25+5.25*k` . It may also be `1.25*k+5.25.`

a. Then we see that the number `1.25` (the free term) is in dollars (or other currency) and it represents the fixed cost. The number `5.25` is in dollars by kilometer and it represents the cost per each kilometer driven.

b. It is not difficult to make the table of values, just substitute different values of k to the formula.

k |    0   |    1   |    2    |    3     |    4    |    5    |    6     |    7    |    8     |    9    |    10     |
A | 1.25 | 6.50 | 11.75 | 17.00 | 22.25 | 27.50 | 32.75 | 38.00 | 43.25 | 48.50 | 53.75 |

Of course each next value is `5.25` greater than the previous.

c. The graph is attached. Of course this relation is linear (the formula is in the slope-intercept form).

d. The graph shows that for 7.5 km one will be charged \$40.625 (probably `\$40.63` ).

e. The graph shows that for `\$15` a person can go as far as about `2.6` km.

Of course the results d and e may be found analytically, too. [Tell me if you need this or if the formula is actually 1.25*k+5.25.]

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