To find the coordinate pair that keeps the ratio equivalent based on the given points, we first need to understand the relationship between x-values and y-values in your data points.
The points given are:
- (2, 3)
- (4, 6)
- (6, 9)
- (8, 12)
Looking at these points, we can analyze the ratio of x to y:
- For the point (2, 3), the ratio \( x:y = 2:3 \)
- For the point (4, 6), the ratio \( x:y = 4:6 \) which simplifies to \( 2:3 \)
- For the point (6, 9), the ratio \( x:y = 6:9 \) which simplifies to \( 2:3 \)
- For the point (8, 12), the ratio \( x:y = 8:12 \) which simplifies to \( 2:3 \)
Thus, the common ratio for all the points is \( 2:3 \).
To find a coordinate pair that maintains this ratio, we can express y in terms of x: \[ \frac{x}{y} = \frac{2}{3} \implies y = \frac{3}{2} x \]
Now, checking the provided coordinate pairs against this equation:
-
(9, 15): \[ y = \frac{3}{2} \times 9 = 13.5 \quad \text{(not equivalent)} \]
-
(15, 10): \[ y = \frac{3}{2} \times 15 = 22.5 \quad \text{(not equivalent)} \]
-
(10, 15): \[ y = \frac{3}{2} \times 10 = 15 \quad \text{(equivalent)} \]
-
(10, 14): \[ y = \frac{3}{2} \times 10 = 15 \quad \text{(not equivalent)} \]
The only coordinate pair that maintains the equivalent ratio \( 2:3 \) is:
(10, 15)