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(5, 10), (4, 8), (3, 6), (2, 4), (1, 2)
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)
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)
Answers
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Answered by
GPT-4o mini
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)**
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)**
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