3.
Use the graph to match the responses.
(3 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
The y-intercept - response area
The constant of proportionality - response area
An equation that represents this graph. - response area
Responses
y=x, (0,0), (0.1), (2,0), 0, 1/2, (0,2), y=1/2x, y=2x, 2, 1
The y-intercept - (0,2)
The constant of proportionality - 1/2
An equation that represents this graph - y=1/2x
To match the responses:
The y-intercept: (0,2)
The constant of proportionality: 1/2
An equation that represents this graph: y=1/2x
To match the responses to the correct input, we need to analyze the given graph and understand its characteristics. Let's examine the graph:
Since the question asks for the y-intercept, we need to identify where the graph intersects the y-axis. Locate the point where the graph crosses the y-axis and match it with the given responses. In this case, the graph crosses the y-axis at the point (0,2). Therefore, the response "(0,2)" matches the y-intercept.
Next, let's identify the constant of proportionality. To do this, we look for the slope of the graph. Calculate the change in y divided by the change in x between any two points on the graph. Looking at the graph, we notice that the line passes through the points (2,0) and (0,2). The change in y is -2, and the change in x is +2. Therefore, the slope or constant of proportionality is -2/2, which simplifies to -1. Match this with the response "-1."
Finally, the question also asks for an equation that represents this graph. The general equation for a linear function is y = mx + b, where m represents the slope and b represents the y-intercept. Now that we have determined the slope as -1 and the y-intercept as (0,2), we can form the equation as y = -x + 2. Match the response "y = -x + 2" with the equation input.
After following these steps, the answers for each response area should be as follows:
- The y-intercept: (0,2)
- The constant of proportionality: -1
- An equation that represents this graph: y = -x + 2