Question

this graph shows a proportional relationship.



What is the constant of proportionality?

Enter your answer as a ratio in simplified form by filling in the boxes.

$$
(2/3, 3/4)

Answer 1

To find the constant of proportionality given the points \((\frac{2}{3}, \frac{3}{4})\), we can use the formula:

\[
k = \frac{y}{x}
\]

where \(k\) is the constant of proportionality, \(y\) is the second value of the point, and \(x\) is the first value of the point.

Using the values from the point:

\[
x = \frac{2}{3}
\]
\[
y = \frac{3}{4}
\]

Now, we can substitute these values into the formula:

\[
k = \frac{\frac{3}{4}}{\frac{2}{3}}
\]

To divide fractions, we multiply by the reciprocal of the divisor:

\[
k = \frac{3}{4} \times \frac{3}{2} = \frac{3 \times 3}{4 \times 2} = \frac{9}{8}
\]

Thus, the constant of proportionality is:

\[
\frac{9}{8}
\]

This is already in simplified form.

So, the answer is:

\[
\text{Constant of proportionality: } \frac{9}{8}
\]