3. %0D%0A%0D%0AUse the graph to match the responses.%0D%0A%0D%0A(3 points)%0D%0APut 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.%0D%0AThe y-intercept%0D%0AThe constant of proportionality%0D%0AAn equation that represents this graph.%0D%0Ay = x21(2, 0)y = 2x0(0, 1)y = 1/2x1/2(0, 2)(0, 0)
The y-intercept: (0, 2)
The constant of proportionality: 1/2
An equation that represents this graph: y = 1/2x
To match the responses with the corresponding inputs, follow these steps:
1. The y-intercept: (0, 2)
- Select the response "y = 2x" and insert it in the input for the y-intercept.
2. The constant of proportionality: (0, 1)
- Select the response "y = 1/2x" and insert it in the input for the constant of proportionality.
3. An equation that represents this graph: (2, 0)
- Select the response "y = x2" and insert it in the input for the equation representing the graph.
After following these steps, you should have the correct matches between the responses and the inputs.
To match the responses to the correct input, we need to understand what each term refers to in the context of the given graph.
1. The y-intercept: The y-intercept is the value of y when x equals zero. It represents the point where the graph intersects the y-axis.
2. The constant of proportionality: The constant of proportionality is a value that relates the input variable, x, to the output variable, y, in a linear equation or graph. It determines the slope of the line.
3. An equation that represents this graph: This requires finding the equation of the line that matches the given graph.
Now let's examine the options and identify which response matches each term:
1. The y-intercept:
- The point (0, 2) on the graph corresponds to the value of y when x equals zero. Therefore, this point represents the y-intercept.
- The response "y = 2x" matches the y-intercept.
2. The constant of proportionality:
- The point (2, 0) on the graph has a y-value of zero when x equals 2. This indicates that the slope of the line is zero, meaning there is no constant of proportionality in this case.
- The response "0" matches the constant of proportionality.
3. An equation that represents this graph:
- Examining the coordinates of the given points on the graph, we see that the point (2, 0) and (0, 2) lie on the line. This suggests that the line passes through these points.
- We can use the two-point form formula to find the equation of the line:
y - y1 = (y2 - y1) / (x2 - x1) * (x - x1)
Plugging in the values (x1 = 2, y1 = 0) and (x2 = 0, y2 = 2), we get:
y - 0 = (2 - 0) / (0 - 2) * (x - 2)
Simplifying it further:
y = 2/2 * (x - 2)
This equation simplifies to:
y = x - 2
- The response "y = x - 2" matches the equation that represents the graph.
So, the matching responses are:
- The y-intercept: y = 2x
- The constant of proportionality: 0
- An equation that represents this graph: y = x - 2