To find the slope of the proportional relationship shown in the table, we can use the formula for slope:
\[ \text{slope} = \frac{\Delta y}{\Delta x} \]
We can use any two points from the table. Let's take the points (0, 0) and (2, 10) as an example.
Calculating the change in \(y\) and \(x\):
\[ \Delta y = 10 - 0 = 10 \]
\[ \Delta x = 2 - 0 = 2 \]
Now, we can find the slope:
\[ \text{slope} = \frac{10}{2} = 5 \]
You can also check with other pairs of points, such as (4, 20) and (2, 10):
\[ \Delta y = 20 - 10 = 10 \]
\[ \Delta x = 4 - 2 = 2 \]
Again:
\[ \text{slope} = \frac{10}{2} = 5 \]
So, the slope of the proportional relationship shown in the table is \(5\).
The slope is 5.