To determine the answers, let’s analyze each part step by step using the answer choices provided.
a. The constant of proportionality refers to the ratio between two quantities that are in a proportional relationship. This is often defined as the coefficient of \(y\) when expressing \(y\) in terms of \(x\) (like in the equation form \(y = kx\), where \(k\) is the constant). If we are looking at \(y = 5x\) or \(5y = x\), then the constant of proportionality can be deduced from those equations.
For \(y = 5x\), the constant of proportionality is \(5\).
For \(5y = x\), we can rearrange it to \(y = \frac{1}{5}x\), and in this case, the constant of proportionality is \(\frac{1}{5}\).
Without specific context from a graph or a relationship being defined, we cannot definitively choose between \(5\) or \(\frac{1}{5}\) for part (a).
b. An equation representing the linear graph can be either \(y = 5x\) or its equivalent forms, depending on which constant you've selected as the multiplicative factor. If we assume this is based on \(y = 5x\), then that’s one option, but \(2y = x\) can also represent a linear relationship.
c. This can be assessed based on the description given. If a graph has a y-intercept at (0,0), has a constant rate of change, and shows a linear relationship, it suggests a proportional relationship indicative of direct variation. The points being connected also indicate it is linear.
So we can summarize the answers considering typical properties of linear graphs:
a. 1/2 (assuming we're using \(5y = x\)) b. y = 5x (similar if using the first option) c. a constant rate of change (because the graph shows a constant increase of \(y\) over \(x\))
Ultimately, specifying more about the values (like \(x\) and \(y\)) would help clarify this further.
2 answers