In order to determine the constant of proportionality, we need to divide the quantities from the \(\displaystyle X\) coordinate by the quantities from the \(\displaystyle Y\) coordinate. In order for the graph to show a direct proportion, each quotient should equal the same value. 

First, we need to find a series of coordinate points:

Now that we have a series of coordinate points, we can divide to find the constant of proportionality:

\(\displaystyle 9\div1=9\)

\(\displaystyle 27\div3=9\)

\(\displaystyle 54\div6=9\)

All of the quotients are the same value; therefore, this graph does show direct proportion and the constant of proportionality is \(\displaystyle 9\).

In order to determine the constant of proportionality, we need to divide the quantities from the \(\displaystyle X\) coordinate by the quantities from the \(\displaystyle Y\) coordinate. In order for the graph to show a direct proportion, each quotient should equal the same value. 

First, we need to find a series of coordinate points:

Now that we have a series of coordinate points, we can divide to find the constant of proportionality:

\(\displaystyle 11\div1=11\)

\(\displaystyle 22\div2=11\)

\(\displaystyle 33\div3=11\)

All of the quotients are the same value; therefore, this graph does show direct proportion and the constant of proportionality is \(\displaystyle 11\).

In order to determine the constant of proportionality, we need to divide the quantities from the \(\displaystyle X\) coordinate by the quantities from the \(\displaystyle Y\) coordinate. In order for the graph to show a direct proportion, each quotient should equal the same value. 

First, we need to find a series of coordinate points:

Now that we have a series of coordinate points, we can divide to find the constant of proportionality:

\(\displaystyle 13\div1=13\)

\(\displaystyle 26\div2=13\)

\(\displaystyle 39\div3=13\)

All of the quotients are the same value; therefore, this graph does show direct proportion and the constant of proportionality is \(\displaystyle 13\).

In order to determine the constant of proportionality, we need to divide the quantities from the \(\displaystyle X\) coordinate by the quantities from the \(\displaystyle Y\) coordinate. In order for the graph to show a direct proportion, each quotient should equal the same value. 

First, we need to find a series of coordinate points:

Now that we have a series of coordinate points, we can divide to find the constant of proportionality:

\(\displaystyle 12\div1=12\)

\(\displaystyle 24\div2=12\)

\(\displaystyle 36\div3=12\)

All of the quotients are the same value; therefore, this graph does show direct proportion and the constant of proportionality is \(\displaystyle 12\).

In order to determine the constant of proportionality, we need to divide the quantities from the \(\displaystyle X\) coordinate by the quantities from the \(\displaystyle Y\) coordinate. In order for the graph to show a direct proportion, each quotient should equal the same value. 

First, we need to find a series of coordinate points:

Now that we have a series of coordinate points, we can divide to find the constant of proportionality:

\(\displaystyle 8\div1=8\)

\(\displaystyle 16\div2=8\)

\(\displaystyle 24\div3=8\)

All of the quotients are the same value; therefore, this graph does show direct proportion and the constant of proportionality is \(\displaystyle 8\).

In order to determine the constant of proportionality, we need to divide the quantities from the \(\displaystyle X\) coordinate by the quantities from the \(\displaystyle Y\) coordinate. In order for the graph to show a direct proportion, each quotient should equal the same value. 

First, we need to find a series of coordinate points:

Now that we have a series of coordinate points, we can divide to find the constant of proportionality:

\(\displaystyle 7\div1=7\)

\(\displaystyle 14\div2=7\)

\(\displaystyle 21\div3=7\)

All of the quotients are the same value; therefore, this graph does show direct proportion and the constant of proportionality is \(\displaystyle 7\).

In order to determine the constant of proportionality, we need to divide the quantities from the \(\displaystyle X\) coordinate by the quantities from the \(\displaystyle Y\) coordinate. In order for the graph to show a direct proportion, each quotient should equal the same value. 

First, we need to find a series of coordinate points:

Now that we have a series of coordinate points, we can divide to find the constant of proportionality:

\(\displaystyle 5\div1=5\)

\(\displaystyle 10\div2=5\)

\(\displaystyle 15\div3=5\)

All of the quotients are the same value; therefore, this graph does show direct proportion and the constant of proportionality is \(\displaystyle 5\).

In order to determine the constant of proportionality, we need to divide the quantities from the \(\displaystyle X\) coordinate by the quantities from the \(\displaystyle Y\) coordinate. In order for the graph to show a direct proportion, each quotient should equal the same value. 

First, we need to find a series of coordinate points:

Now that we have a series of coordinate points, we can divide to find the constant of proportionality:

\(\displaystyle 3\div1=3\)

\(\displaystyle 15\div5=3\)

\(\displaystyle 21\div7=3\)

All of the quotients are the same value; therefore, this graph does show direct proportion and the constant of proportionality is \(\displaystyle 3\).

In order to determine the constant of proportionality, we need to divide the quantities from the \(\displaystyle X\) coordinate by the quantities from the \(\displaystyle Y\) coordinate. In order for the graph to show a direct proportion, each quotient should equal the same value. 

First, we need to find a series of coordinate points:

Now that we have a series of coordinate points, we can divide to find the constant of proportionality:

\(\displaystyle 10\div1=10\)

\(\displaystyle 20\div2=10\)

\(\displaystyle 30\div3=10\)

All of the quotients are the same value; therefore, this graph does show direct proportion and the constant of proportionality is \(\displaystyle 10\).

In order to determine the constant of proportionality, we need to divide the quantities from the y-coordinate by the quantities from the x-coordinate. In order for the graph to show a direct proportion, each quotient should equal the same value. 

First, we need to find a series of coordinate points:

Now that we have a series of coordinate points, we can divide the y-coordinate of each by its corresponding x-coordinate to find the constant of proportionality:

For point (4, 1), 1 divided by 4 is \(\displaystyle \frac{1}{4}\)

For point (8, 2), 2 divided by 8 is \(\displaystyle \frac{1}{4}\)

For point (12, 3), 3 divided by 12 is \(\displaystyle \frac{1}{4}\)

All of the quotients are the same value; therefore, this graph does show direct proportion and the constant of proportionality is \(\displaystyle \frac{1}{4}\).