Question

Please I need help with this!!

Determine whether y varies directly with x. If so find the constant of variation k and write the equation.

Answer 1

Constant: 1.6

y ÷ x = k

Explanation:

Divide y by x

6.4 ÷ 4 = 1.6

11.2 ÷ 7 = 1.6

16 ÷ 10 = 1.6

20.8 ÷ 13 = 1.6

1.6 is the constant of proportionality.

Dividing y by x = k. And k is the constant of proportionality.

Answer 2

Yes, y varies directly with x because ratio of y to x is the same for all pairs of data points

Constant of variation: k = 1.6

Equation: y = 1.6x

Explanation:

To determine whether y varies directly with x, we can check to see if the ratio of y to x is constant for all pairs of data points:

`\sf (y)/(x)=(6.4)/(4)=1.6`

`\sf (y)/(x)=(11.2)/(7)=1.6`

`\sf (y)/(x)=(16)/(10)=1.6`

`\sf (y)/(x)=(20.8)/(13)=1.6`

Since the ratio of y to x is the same for all pairs of data points, we can conclude that y varies directly with x.

The constant of variation, k, is equal to the ratio of any pair of data points.

In this case,

we can use the first pair of data points to find k:

`\sf k = (y)/(x)=(6.4)/(4)=1.6`

Therefore, the equation of the relationship between y and x is:

y = 1.6x