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6-11.

PROPORTIONAL RELATIONSHIPS

In parts (a) through (d) below, decide whether the two given quantities are proportional. If they are, write an equation relating them and state the proportionality constant $k$. If they are not, explain why not.

Example: Distance $d$ traveled (in miles) when driving for $t$ hours at a constant speed of $50$ mph. Solution: $d = 50t$, with $k = 50$.

1. Cost $c$ in dollars of $n$ chocolate bars at $50$ cents each.

$c$ and $n$ are proportional
$c = 0.50n$

1. Number of hours $t$ that it takes to drive $50$ miles at $r$ miles per hour.

distance $=$ (rate)(time)
Is rate proportional to time?

1. Taxi fare $f$ depends on the number of miles $m$ driven. The fare is $2$ for the first mile, then $1$ for each subsequent mile.

Write an equation for the total taxi fare.
Is this a proportional relationship?

1. Time $t$ it takes to read $n$ mysteries if each book takes $10$ hours to read.

$t = 10n$
Is this a proportional relationship?