Question
This is a proportional or non proportional
relationship? The y-intercept is? 2 , 1/2 , (1,0) , (0,1)?
and the slope is 2 , 1/2 , (1,0) , (0,1)?
The equation of the line is slope-intercept form is y=1x+2 , y=1/2x+1 , y=2x+1 , y=1/2x?
Answers
Answered by
GPT 3.5
A proportional relationship refers to a linear relationship in which the ratio between the y-values and x-values is constant. On the other hand, a non-proportional relationship does not have a constant ratio.
To determine if the given relationships are proportional or non-proportional, we need to compare the ratio of the y-values to the x-values for each set of coordinates.
For (2, 1/2), the ratio is (1/2) / 2 = 1/4, which is not constant. Therefore, this is a non-proportional relationship.
For (1, 0), the ratio is 0 / 1 = 0, which is constant. Therefore, this is a proportional relationship.
For (0, 1), the ratio is 1 / 0, which is undefined. Therefore, this relationship cannot be determined as proportional or non-proportional based on this single point.
Now let's consider the slope-intercept form of the equations:
y = 1x + 2
y = 1/2x + 1
y = 2x + 1
y = 1/2x
From the equation y = 1x + 2, the y-intercept is 2. This indicates that the line crosses the y-axis at (0, 2).
From the equation y = 1/2x + 1, the y-intercept is 1. This indicates that the line crosses the y-axis at (0, 1).
From the equation y = 2x + 1, the y-intercept is 1. This indicates that the line crosses the y-axis at (0, 1).
From the equation y = 1/2x, there is no explicit constant term, so the y-intercept is 0. This indicates that the line passes through the origin (0, 0).
To summarize:
- The relationship between (2, 1/2) is non-proportional.
- The relationship between (1, 0) is proportional.
- The relationship between (0, 1) cannot be determined as proportional or non-proportional based on a single point.
- The equation of the line y = 1x + 2 has a y-intercept of 2.
- The equation of the line y = 1/2x + 1 has a y-intercept of 1.
- The equation of the line y = 2x + 1 has a y-intercept of 1.
- The equation of the line y = 1/2x has a y-intercept of 0.
To determine if the given relationships are proportional or non-proportional, we need to compare the ratio of the y-values to the x-values for each set of coordinates.
For (2, 1/2), the ratio is (1/2) / 2 = 1/4, which is not constant. Therefore, this is a non-proportional relationship.
For (1, 0), the ratio is 0 / 1 = 0, which is constant. Therefore, this is a proportional relationship.
For (0, 1), the ratio is 1 / 0, which is undefined. Therefore, this relationship cannot be determined as proportional or non-proportional based on this single point.
Now let's consider the slope-intercept form of the equations:
y = 1x + 2
y = 1/2x + 1
y = 2x + 1
y = 1/2x
From the equation y = 1x + 2, the y-intercept is 2. This indicates that the line crosses the y-axis at (0, 2).
From the equation y = 1/2x + 1, the y-intercept is 1. This indicates that the line crosses the y-axis at (0, 1).
From the equation y = 2x + 1, the y-intercept is 1. This indicates that the line crosses the y-axis at (0, 1).
From the equation y = 1/2x, there is no explicit constant term, so the y-intercept is 0. This indicates that the line passes through the origin (0, 0).
To summarize:
- The relationship between (2, 1/2) is non-proportional.
- The relationship between (1, 0) is proportional.
- The relationship between (0, 1) cannot be determined as proportional or non-proportional based on a single point.
- The equation of the line y = 1x + 2 has a y-intercept of 2.
- The equation of the line y = 1/2x + 1 has a y-intercept of 1.
- The equation of the line y = 2x + 1 has a y-intercept of 1.
- The equation of the line y = 1/2x has a y-intercept of 0.