Question

Find the constant of variation and write the equation representing the relationship between the quantities in each of the following.

1. x= 1 ,2 ,3 ,4
y= 2, 1, ⅔, ½

3. x=3, 6, 9, 12
y= 2,1,⅔, ½

7. y varies inversely as x and y=12 when x=5​

Answer 1

To find the constant of variation and write the equation representing the relationship between the quantities in each scenario, observe the pattern in the given data. For the first scenario, the inverse variation equation is y = 1/2x. For the second and third scenarios, the inverse variation equation is y = 1/3x.

Step-by-step explanation:

To find the constant of variation and write the equation representing the relationship between the quantities in each scenario, we need to observe the pattern in the given data.

For the first scenario, as x increases by 1, y decreases by half. This indicates an inverse variation. The constant of variation is 1/2. Therefore, the equation representing the relationship is y = 1/2x.

For the second scenario, as x increases by 3, y decreases by half. This also indicates an inverse variation. The constant of variation is 1/3. Therefore, the equation representing the relationship is y = 1/3x.

For the third scenario, as x increases by 3, y decreases by half. Again, this indicates an inverse variation. The constant of variation is 1/3. Therefore, the equation representing the relationship is y = 1/3x.