To determine the slope of a proportional relationship, we need to calculate the ratio of the change in the vertical or dependent variable to the change in the horizontal or independent variable. Let's observe the table:
\[
\begin{array}{|c|c|}
\hline
\text{Horizontal (x)} & \text{Vertical (y)} \\
\hline
2 & 5 \\
\hline
4 & 10 \\
\hline
6 & 15 \\
\hline
8 & 20 \\
\hline
\end{array}
\]
The ratio of the change in y to the change in x seems to be constant. We can calculate this ratio by examining any two consecutive points. For example, taking the first two points, we observe that the change in y is $10 - 5 = 5$, while the change in x is $4 - 2 = 2$. So, the ratio is $5/2$.
We can also examine the change in y and x for other pairs of points and observe that the ratio is always $5/2$. Therefore, the slope of the proportional relationship shown in the table is $\boxed{\dfrac{5}{2}}$.
Determine the slope of the proportional relationship shown in the table.
1 answer