Question

journal
when a graph shows a
proportional relationship,
explain how the unit rate is
related to the constant of
proportionality.
remember
when the relationship between two quantities
is proportional, the graph of the relationship is a
straight line that passes through the origin. the
point (1, r) represents the unit rate, and the ratio (\frac{r}{1}) represents the constant of proportionality, k.
practice

determine the constant of proportionality k and interpret it in the context of

each problem.
1 the graph shows the relationship between
the distance in miles between you and a
storm and the number of seconds between
when you see lightning and when you
hear thunder.
2 the graph shows the relationship between
the number of euros jason received and
the number of dollars jason exchanged
during his trip to spain.
go to livehint.com for help

Explanation:

Step1: Recall the formula for the constant of proportionality

For a proportional relationship \(y = kx\), the constant of proportionality \(k=\frac{y}{x}\)

Step2: Find \(k\) for the first graph

In the first graph (distance - time), we can use the point \((5,1)\). Substitute \(x = 5\) and \(y = 1\) into the formula \(k=\frac{y}{x}\). So \(k=\frac{1}{5}\). This means that for every second that passes, the distance between you and the storm increases by \(\frac{1}{5}\) of a mile.

Step3: Find \(k\) for the second graph

In the second graph (euros - dollars), we can use the point \((3,4)\). Substitute \(x = 3\) and \(y = 4\) into the formula \(k=\frac{y}{x}\). So \(k = \frac{4}{3}\). This means that for every dollar Jason exchanges, he receives \(\frac{4}{3}\) euros.

Answer:

1. \(k = \frac{1}{5}\)
2. \(k=\frac{4}{3}\)