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)

1 answer

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:

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