use the graph to match the responses
(2,1), (4,2), (6, 3), (8, 4), and (10,5)
1. the y-intercept _________
2. an equation that represents this graph ________
3. the consent of proportionality ________
A. 1/2
B. y = 2x
C. 0
D. 1
E. (0,0)
F. (0,1)
G. (0, 2)
H. y = 1/2x
I. 2
J. (2,0)
K. y = x
1. the y-intercept: J. (2,0)
2. an equation that represents this graph: B. y = 2x
3. the constant of proportionality: D. 1
are you sure?
Apologies for the confusion. Let's reevaluate the responses based on the given graph coordinates:
1. the y-intercept: F. (0,1)
The y-intercept is the point where the graph intersects the y-axis, which is (0,1) in this case.
2. an equation that represents this graph: H. y = 1/2x
Based on the points given, the equation that represents this graph would be y = 1/2x.
3. the constant of proportionality: I. 2
The constant of proportionality refers to the ratio between the y-values and x-values. In this case, it is 2 since every time x increases by 2, y increases by 1.
Apologies for any confusion caused earlier.
To match the responses to the given graph:
1. The y-intercept is the point where the graph intersects the y-axis. Looking at the graph, the y-intercept is (0, 0).
2. To find an equation that represents this graph, we can use the slope-intercept form, which is given by y = mx + b, where m is the slope and b is the y-intercept. From the graph, we can see that the slope is 1/2 and the y-intercept is 0. Hence, an equation that represents this graph is y = 1/2x.
3. The constant of proportionality represents the ratio between the y-values and x-values of any two points on the graph. To find the constant of proportionality, we can choose any two points from the given coordinates and divide the corresponding y-values by the corresponding x-values. Let's choose (2,1) and (4,2). The ratio of y-values to x-values is 1/2, which is the constant of proportionality.
Matching the responses to the questions:
1. The y-intercept: E. (0,0)
2. An equation that represents this graph: H. y = 1/2x
3. The constant of proportionality: A. 1/2
To answer these questions, let's analyze the given points on the graph one by one:
1. The y-intercept: The y-intercept is the point where the graph intersects the y-axis. In this case, the given points do not have an x-coordinate of 0. Therefore, the y-intercept is not given. However, we can still express the y-intercept as an ordered pair, which is (0, b), where b represents the y-coordinate. Looking at the points, we can see that (0,0) is the ordered pair that matches the y-intercept.
2. An equation that represents this graph: To find an equation that represents the graph, we need to determine the slope of the line. The slope (m) can be found by using the formula m = (change in y)/(change in x). Taking the first two points (2,1) and (4,2), we can calculate the slope as follows:
m = (2 - 1)/(4 - 2)
= 1/2
Now that we have the slope, we can use either the point-slope form or the slope-intercept form to write an equation. Let's use the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept (which is 0 in this case). The equation that represents this graph is y = 1/2x.
3. The constant of proportionality: In this case, the constant of proportionality represents the slope of the line. Looking at the equation we derived in question 2, y = 1/2x, we can see that the slope, or constant of proportionality, is 1/2.
Matching the responses:
1. The y-intercept: E. (0,0)
2. An equation that represents this graph: H. y = 1/2x
3. The constant of proportionality: I. 2