Question

4.

Use the graph to match the responses.

(3 points)


The constant of proportionality (blank)

An equation that represents this graph. (blank)

The y-intercept (blank)

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

Answer 1

To match the responses with the options provided, we can analyze each item:

1. **The constant of proportionality**: This is the ratio of \(y\) to \(x\) when the graph represents a proportional relationship (a straight line through the origin). If the line's equation is \(y = \frac{1}{2}x\), then the constant of proportionality is \(\frac{1}{2}\).

2. **An equation that represents this graph**: If the graph corresponds to a line with a constant slope of \(\frac{1}{2}\), the equation would be \(y = \frac{1}{2}x\).

3. **The y-intercept**: The y-intercept is the point where the graph crosses the y-axis. If the graph goes through the origin (0, 0), then the y-intercept is (0, 0).

Now we can fill in the blanks:

- The constant of proportionality: **1/2**
- An equation that represents this graph: **y = 1/2x**
- The y-intercept: **(0, 0)**

So, the answers are:

- The constant of proportionality: **1/2**
- An equation that represents this graph: **y = 1/2x**
- The y-intercept: **(0, 0)**