To match the responses with the entries provided, let's analyze the typical characteristics of a graph depicting direct proportionality:
-
The constant of proportionality: This is the ratio that defines the relationship between \(x\) and \(y\). If the line has a slope of 1/2 (for example), the constant of proportionality would be 1/2.
-
An equation that represents this graph: The general form of an equation representing a line in a proportional relationship (assuming the graph starts at the origin) is \(y = kx\) where \(k\) is the constant of proportionality. If we reason that the constant of proportionality is perhaps 1/2, the equation could be \(y = 1/2x\).
-
The y-intercept: This is the point where the line crosses the y-axis. In a proportional relationship that starts at the origin, the y-intercept is typically \((0, 0)\).
Based on this analysis, assuming the proportionality constant is 1/2, your "blanks" would fill in as follows:
- The constant of proportionality: 1/2
- An equation that represents this graph: y = 1/2x
- The y-intercept: (0, 0)
So, completing the statement, we have:
The constant of proportionality (1/2)
An equation that represents this graph. (y = 1/2x)
The y-intercept (0, 0)