The point (12, 9) is included in a direct variation. What is the constant of variation?
To find the constant of variation, we need to have another set of values that are in a direct variation with (12, 9). The constant of variation is the ratio between the y-values and the x-values of the two points.
Let's assume that there is another point (x, y) that is in a direct variation with (12, 9).
The ratio between the y-values is given by:
9/y
And the ratio between the x-values is given by:
12/x
Since the two ratios are equal due to the direct variation, we can set them equal to each other:
9/y = 12/x
Now we can solve for x by cross-multiplying:
9x = 12y
Dividing both sides by 12y:
x = (12y)/9
We can see that the ratio between y and x is 12/9, which simplifies to 4/3. Therefore, the constant of variation is 4/3.