Question
Line RQ represents a proportional relationship. Point R lies at left bracket, 18, comma, 16, right bracket(18,16) as shown on the graph below.
Which ordered pair could represent the coordinates of point Q?
A. (2,0)
B. (13.5,12)
C. (0.9,0)
D. (4,4.5)
Which ordered pair could represent the coordinates of point Q?
A. (2,0)
B. (13.5,12)
C. (0.9,0)
D. (4,4.5)
Answers
Answered by
GPT 3.5
To determine the coordinates of point Q, we need to find the constant of proportionality between the x and y values of the points on line RQ.
Looking at the graph, we can see that as the x-values increase by 9 (from 9 to 18), the y-values increase by 8 (from 8 to 16).
Therefore, the constant of proportionality is 8/9.
To find the coordinates of point Q, we can use the constant of proportionality to find the change in y for a given change in x. In this case, the change in x is 9.
So, the change in y is (8/9) * 9 = 8.
Starting from the y-value of point R (16), we can add the change in y to find the y-value of point Q.
16 + 8 = 24
Therefore, the y-value of point Q is 24.
Now we need to find the x-value of point Q. Looking at the graph, we can see that as the x-values increase by 9 (from 9 to 18), the y-values increase by 8 (from 8 to 16). This means that for every 1 increase in x, there is a (8/9) increase in y.
So, for a change in y of 8, the corresponding change in x is 9 * (1/8) = 9/8.
Starting from the x-value of point R (18), we can subtract the change in x to find the x-value of point Q.
18 - (9/8) = 162/8 - 9/8 = 153/8 = 19.125
Therefore, the x-value of point Q is 19.125.
The ordered pair that represents the coordinates of point Q is (19.125, 24).
None of the given options match this ordered pair, so the correct answer is None of the above.
Looking at the graph, we can see that as the x-values increase by 9 (from 9 to 18), the y-values increase by 8 (from 8 to 16).
Therefore, the constant of proportionality is 8/9.
To find the coordinates of point Q, we can use the constant of proportionality to find the change in y for a given change in x. In this case, the change in x is 9.
So, the change in y is (8/9) * 9 = 8.
Starting from the y-value of point R (16), we can add the change in y to find the y-value of point Q.
16 + 8 = 24
Therefore, the y-value of point Q is 24.
Now we need to find the x-value of point Q. Looking at the graph, we can see that as the x-values increase by 9 (from 9 to 18), the y-values increase by 8 (from 8 to 16). This means that for every 1 increase in x, there is a (8/9) increase in y.
So, for a change in y of 8, the corresponding change in x is 9 * (1/8) = 9/8.
Starting from the x-value of point R (18), we can subtract the change in x to find the x-value of point Q.
18 - (9/8) = 162/8 - 9/8 = 153/8 = 19.125
Therefore, the x-value of point Q is 19.125.
The ordered pair that represents the coordinates of point Q is (19.125, 24).
None of the given options match this ordered pair, so the correct answer is None of the above.