Answer:
A. Yes, because there is a constant rate of 2.
Step-by-step explanation:
A proportional linear equation describes a relationship between two variables where one is directly proportional to the other. In other words, as one variable changes, the other changes in direct proportion to it.
[tex]\boxed{\begin{array}{l}\underline{\textsf{Proportional linear equation}}\\\\y=kx\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$y$ is the dependent variable.}\\\phantom{ww}\bullet\;\textsf{$x$ is the independent variable.}\\\phantom{ww}\bullet\;\textsf{$k$ is the constant of proportionality.}\end{array}}[/tex]
As x increases or decreases, y changes in direct proportion to x. The constant k represents the ratio between y and x, indicating how much y changes for each unit change in x.
If we substitute x = 0 into a proportional linear equation, we get y = 0, so the graph of a proportional linear equation will always contain point (0, 0).
To determine if the relationship between x and y is proportional, calculate the ratio of y to x for each row of the table. If the ratio is the same for all rows, the relationship is proportional:
[tex]\dfrac{4}{2}=2\\\\\\\dfrac{6}{3}=2\\\\\\\dfrac{10}{5}=2\\\\\\\dfrac{12}{6}=2\\\\\\\dfrac{16}{8}=2[/tex]
So, the constant of proportionality is 2, and so the equation of the relationship is y = 2x.
Therefore, the relationship is proportional because:
- The ratios of y/x of each row of the table are the same.
- The graph passes through the origin (0, 0).
