Which graph shows a constant of proportionality of 4?
A. x=1 y=4, x=3 y=12
B. x=1 y=2, x=3 y=6
C. x=1 y=6, x=2 y=12
D. x=1 y=8, x=2 y=16
To determine which graph shows a constant of proportionality of 4, we need to identify the relationship between the x-values and y-values in each option.
A constant of proportionality means that the ratio of y-values to x-values is constant throughout. In other words, for every increase of 1 in the x-value, the y-value increases by a constant factor.
Let's analyze each option:
A. x=1 y=4, x=3 y=12: In this option, when x increases by 2 (from 1 to 3), the y-value increases by 8 (from 4 to 12). The ratio of the change in y to the change in x is 8/2 = 4. This option satisfies the condition for a constant of proportionality.
B. x=1 y=2, x=3 y=6: In this option, when x increases by 2 (from 1 to 3), the y-value increases by 4 (from 2 to 6). The ratio of the change in y to the change in x is 4/2 = 2. This option does not satisfy the condition for a constant of proportionality.
C. x=1 y=6, x=2 y=12: In this option, when x increases by 1 (from 1 to 2), the y-value increases by 6 (from 6 to 12). The ratio of the change in y to the change in x is 6/1 = 6. This option does not satisfy the condition for a constant of proportionality.
D. x=1 y=8, x=2 y=16: In this option, when x increases by 1 (from 1 to 2), the y-value increases by 8 (from 8 to 16). The ratio of the change in y to the change in x is 8/1 = 8. This option does not satisfy the condition for a constant of proportionality.
From the above analysis, we can conclude that option A (x=1 y=4, x=3 y=12) shows a constant of proportionality of 4.