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.
$$
A graph with a line running through coordinates left parenthesis 0 comma 0 right parenthesis and coordinates left parenthesis 2 over 3 end fraction comma 3 over 4 end fraction right parenthesis.
What is the constant of proportionality?
Enter your answer as a ratio in simplified form by filling in the boxes.
$$
A graph with a line running through coordinates left parenthesis 0 comma 0 right parenthesis and coordinates left parenthesis 2 over 3 end fraction comma 3 over 4 end fraction right parenthesis.
Answers
GPT-4o mini
To find the constant of proportionality from the given points, you can use the formula for the constant of proportionality \( k \):
\[
k = \frac{y}{x}
\]
From the graph, the coordinates given are \((x, y) = \left(\frac{2}{3}, \frac{3}{4}\right)\).
Now we can calculate \( k \):
\[
k = \frac{y}{x} = \frac{\frac{3}{4}}{\frac{2}{3}} = \frac{3}{4} \times \frac{3}{2} = \frac{3 \times 3}{4 \times 2} = \frac{9}{8}
\]
Thus, the constant of proportionality is:
\[
\frac{9}{8}
\]
In simplified form, it is \( 9 \) in the numerator box and \( 8 \) in the denominator box.
\[
k = \frac{y}{x}
\]
From the graph, the coordinates given are \((x, y) = \left(\frac{2}{3}, \frac{3}{4}\right)\).
Now we can calculate \( k \):
\[
k = \frac{y}{x} = \frac{\frac{3}{4}}{\frac{2}{3}} = \frac{3}{4} \times \frac{3}{2} = \frac{3 \times 3}{4 \times 2} = \frac{9}{8}
\]
Thus, the constant of proportionality is:
\[
\frac{9}{8}
\]
In simplified form, it is \( 9 \) in the numerator box and \( 8 \) in the denominator box.