(5, 10), (4, 8), (3, 6), (2, 4), (1, 2)

Question

Use the graph to match the responses.
An equation that represents this graph. _________________
The constant of proportionality _________________
The y-intercept ________________
Options: 2, (0, 2), (2, 0), (0, 0), 1, 0, y = 2x, y = 1/2x, 1/2, y = x, (0, 1)

Answer 1

To determine the correct responses, let's analyze the given points and their relationships. The points are (5, 10), (4, 8), (3, 6), (2, 4), and (1, 2).

1. Equation that represents the graph:
   The points suggest a linear relationship of the form \( y = mx \), where \( m \) is the slope. To calculate the slope (constant of proportionality) between any two points:

   • Using points (1, 2) and (5, 10): \[ m = \frac{10 - 2}{5 - 1} = \frac{8}{4} = 2 \] Thus, the equation is: \[ y = 2x \]

2. The constant of proportionality:
   The constant of proportionality is the slope \( m \), which we found to be 2.

3. The y-intercept:
   The y-intercept is the value of \( y \) when \( x = 0 \). Since the relationship is linear and goes through the origin with the equation \( y = 2x \), the y-intercept is indeed (0, 0).

Now, matching these to the options provided, we can summarize:

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

Thus:

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