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4.

Use the graph to match the responses.

The constant of proportionality (BLANK)

An equation that represents this graph. (BLANK)

The y-intercept (BLANK)

options for the "blanks", 0, 2, (0, 2), 1/2, (0, 0), (2, 0), y = x, (0, 1), y = 1/2x, y = 2x, 1

1 answer

To match the responses with the entries provided, let's analyze the typical characteristics of a graph depicting direct proportionality:

  1. 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.

  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 \(y = 1/2x\).

  3. 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:

  1. The constant of proportionality: 1/2
  2. An equation that represents this graph: y = 1/2x
  3. 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)