To find a coordinate pair that maintains the ratio consistent with the given points on the line, we should first determine the relationship between the x-values and y-values.
From the points provided:
- The first point is (2, 3).
- The fourth point is (8, 12).
We can observe the following:
- The x-values are 2, 4, 6, 8 — increasing by 2.
- The y-values are 3, 6, 9, 12 — increasing by 3.
From this, we can see that for every increase of 2 in the x-value, there is an increase of 3 in the y-value. This gives us a consistent ratio of:
\[ \frac{y}{x} = \frac{3}{2} \quad \text{or} \quad y = \frac{3}{2}x. \]
Now, let’s check the provided response options to see which pair maintains this ratio:
-
(4, 6): \[ \frac{6}{4} = \frac{3}{2} \quad \text{(Valid)} \]
-
(4, 8): \[ \frac{8}{4} = 2 \quad \text{(Not valid)} \]
-
(6, 4): \[ \frac{4}{6} = \frac{2}{3} \quad \text{(Not valid)} \]
-
(8, 4): \[ \frac{4}{8} = \frac{1}{2} \quad \text{(Not valid)} \]
-
(4, 10): \[ \frac{10}{4} = \frac{5}{2} \quad \text{(Not valid)} \]
-
(3, 8): \[ \frac{8}{3} \quad \text{(Not valid)} \]
Based on this analysis, the only valid coordinate pair that maintains the ratio is:
(4, 6)