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4. Use the graph to match the responses. (3 points) An equation that represents this graph. The y-intercept The constant of proportionality

Look at this imaginary graph we have the y-intercept and x-intercept the pin pointed points are in the top right box of the graph theres 4 boxes but were focusing on the top right one, the pin point points are going in a diagnol line, the y line lists Miles walked as the x line lists hours, the pin point diagnol line starts at 2 4 6 8, and ends at 10

7 answers

To match the responses based on the description of the graph you provided, let's address each of the components:

  1. An equation that represents this graph: If the graph depicts a diagonal line starting from the y-axis, we can determine the slope (rate of change) and the y-intercept. Given the coordinates you mentioned (4, 2), (6, 4), (8, 6), and (10, 8), the relationship appears to be linear, and can be represented as \(y = mx + b\).

    To find the slope (\(m\)): \[ m = \frac{\Delta y}{\Delta x} = \frac{4 - 2}{6 - 4} = 1 \]

    Therefore, the equation becomes: \[ y = x - 2 \]

  2. The y-intercept: The y-intercept is the value of \(y\) when \(x = 0\). From the given points, it appears that the line intersects the y-axis at \(y = -2\). Thus, the y-intercept is: \[ -2 \]

  3. The constant of proportionality: In the context of slope/linear equations, the constant of proportionality refers to the slope \(m\). Here, from the earlier calculation, we found that the slope is 1. So, the constant of proportionality is: \[ 1 \]

To summarize, based on your graph:

  • The equation that represents the graph is \(y = x - 2\).
  • The y-intercept is \(-2\).
  • The constant of proportionality is \(1\).
this imaginary line starts at the origin going diagonally to the right going straight

Thank you for the clarification! If the imaginary line starts at the origin (0,0) and goes diagonally to the right, it indicates a direct proportional relationship between the two variables: hours and miles walked.

Here’s how we can summarize the match:

  1. An equation that represents this graph: Since the line starts at the origin and increases diagonally, the equation is typically of the form: \[ y = mx \] If the points mentioned (2, 4), (4, 8), etc., suggest that for every 2 hours, 4 miles are walked, it means the slope (constant of proportionality) is 2. Therefore, the equation can be written as: \[ y = 2x \]

  2. The y-intercept: The y-intercept is the point where the line crosses the y-axis. Since the line starts at the origin (0,0), the y-intercept is: \[ 0 \]

  3. The constant of proportionality: The constant of proportionality is equal to the slope of the line. In this case, the constant of proportionality (slope) is: \[ 2 \]

To summarize, based on your description of the imaginary graph:

  • The equation that represents the graph is \(y = 2x\).
  • The y-intercept is \(0\).
  • The constant of proportionality is \(2\).
so is that like (0,0) and (0,2) (2,0) or just 0 and 2

Let's clarify the terminology and the points based on your earlier description of the graph.

  1. (0,0): This point is where the line starts, known as the origin. Here, when \(x = 0\) (0 hours), \(y = 0\) (0 miles walked).

  2. The y-intercept: This is identified by the point where the line crosses the y-axis. In your case, since the line starts at the origin, when \(x = 0\), the corresponding \(y\) value is also 0. So the y-intercept is at the point (0, 0).

  3. Constant of proportionality: If the equation representing the relationship is \(y = mx\), where \(m\) is the constant of proportionality, in your example it appears to be \(2\), which means for every hour walked, if \(m\) is 2, the equation would be \(y = 2x\). This means for every hour, the distance in miles increases by 2.

  4. Key points:

    • If you plotted this on a graph, some example points would be:
      • (0, 0) when 0 hours are walked, 0 miles are walked.
      • (1, 2) when 1 hour is walked, 2 miles are walked.
      • (2, 4) when 2 hours are walked, 4 miles are walked.
      • (3, 6) when 3 hours are walked, 6 miles are walked.

To summarize:

The important points based on your equation \(y = 2x\) would specifically be:

  • The y-intercept is 0 (this point is (0,0)).
  • The constant of proportionality is 2.

So, the points you're asking about like (0,2) or (2,0) would not apply here, as in the context we discussed the key point on the y-axis is simply (0,0), with the line defined by the equation representing the relationship between hours and miles walked.

so do I place 0,0 or 0 there

In the context of identifying and placing values based on your graph:

  1. For the y-intercept: You would put 0. This indicates the y-value where the line crosses the y-axis, which is at the point (0, 0).

  2. For the point itself: If you were to list the coordinate of the y-intercept, it would be (0, 0).

So if you need to specify just the y-intercept, you would place 0. If you need to specify the coordinate as a point on the graph, you would write it as (0, 0).

Summary:

  • If asked for just the y-intercept: 0
  • If asked for the y-intercept as a coordinate: (0, 0)