Question
4.
Use the graph to match the responses.
The constant of proportionality (BLANK)
An equation that represents this graph. (BLANK)
The y-intercept (BLANK)
options for the "blanks", 0, 2, (0, 2), 1/2, (0, 0), (2, 0), y = x, (0, 1), y = 1/2x, y = 2x, 1
Use the graph to match the responses.
The constant of proportionality (BLANK)
An equation that represents this graph. (BLANK)
The y-intercept (BLANK)
options for the "blanks", 0, 2, (0, 2), 1/2, (0, 0), (2, 0), y = x, (0, 1), y = 1/2x, y = 2x, 1
Answers
Answered by
GPT-4o mini
To match the responses with the entries provided, let's analyze the typical characteristics of a graph depicting direct proportionality:
1. **The constant of proportionality**: This is the ratio that defines the relationship between \(x\) and \(y\). If the line has a slope of 1/2 (for example), the constant of proportionality would be 1/2.
2. **An equation that represents this graph**: The general form of an equation representing a line in a proportional relationship (assuming the graph starts at the origin) is \(y = kx\) where \(k\) is the constant of proportionality. If we reason that the constant of proportionality is perhaps 1/2, the equation could be \(y = 1/2x\).
3. **The y-intercept**: This is the point where the line crosses the y-axis. In a proportional relationship that starts at the origin, the y-intercept is typically \((0, 0)\).
Based on this analysis, assuming the proportionality constant is 1/2, your "blanks" would fill in as follows:
1. **The constant of proportionality**: **1/2**
2. **An equation that represents this graph**: **y = 1/2x**
3. **The y-intercept**: **(0, 0)**
So, completing the statement, we have:
The constant of proportionality (1/2)
An equation that represents this graph. (y = 1/2x)
The y-intercept (0, 0)
1. **The constant of proportionality**: This is the ratio that defines the relationship between \(x\) and \(y\). If the line has a slope of 1/2 (for example), the constant of proportionality would be 1/2.
2. **An equation that represents this graph**: The general form of an equation representing a line in a proportional relationship (assuming the graph starts at the origin) is \(y = kx\) where \(k\) is the constant of proportionality. If we reason that the constant of proportionality is perhaps 1/2, the equation could be \(y = 1/2x\).
3. **The y-intercept**: This is the point where the line crosses the y-axis. In a proportional relationship that starts at the origin, the y-intercept is typically \((0, 0)\).
Based on this analysis, assuming the proportionality constant is 1/2, your "blanks" would fill in as follows:
1. **The constant of proportionality**: **1/2**
2. **An equation that represents this graph**: **y = 1/2x**
3. **The y-intercept**: **(0, 0)**
So, completing the statement, we have:
The constant of proportionality (1/2)
An equation that represents this graph. (y = 1/2x)
The y-intercept (0, 0)