Answer: Here's my answer
Explanation:
he representation that has a constant of variation of -2.5 is Option 2: b x 4 6 8 10 y -10 -15 -20 -25.
A constant of variation represents how the dependent variable (y) changes in relation to the independent variable (x). In this case, a constant of -2.5 means that for every unit increase in x, y decreases by 2.5 units.
Looking at Option 2, we can see that as x increases by 2 units (from 4 to 6), y decreases by 5 units (from -10 to -15). Similarly, as x increases by 2 units (from 6 to 8), y decreases by 5 units (from -15 to -20), and so on.
This consistent decrease of 5 units for every 2 unit increase in x confirms that Option 2 has a constant of variation of -2.5.
The other options do not have a constant of variation of -2.5:
- Option 1 has a constant of variation of -2, as y decreases by 2 units for every 1 unit increase in x.
- Option 3 does not show a clear relationship between x and y, as it only provides a single point.
- Option 4 represents a line on a coordinate plane, but it does not have a constant of variation of -2.5. To determine the constant of variation, we need to know the relationship between x and y for the entire line, which is not provided.
Therefore, Option 2: b x 4 6 8 10 y -10 -15 -20 -25 is the representation with a constant of variation of -2.5.