Determine whether y varies directly with x. If so find the constant of variation k and write the equation.
x y
4 6.4
7. 11.2
10 16
13. 20.8
Yes, y varies directly with x. The constant of variation k is 2.4 and the equation is y = 2.4x.
Could you show the steps please
Hello?
To determine whether y varies directly with x, we need to check if the ratio of y to x remains constant.
We can calculate the ratio for each pair of x and y values:
For the first pair (4, 6.4), the ratio is 6.4 / 4 = 1.6.
For the second pair (7, 11.2), the ratio is 11.2 / 7 ≈ 1.6.
For the third pair (10, 16), the ratio is 16 / 10 = 1.6.
For the fourth pair (13, 20.8), the ratio is 20.8 / 13 ≈ 1.6.
Since the ratio remains constant at 1.6 for all pairs, we can conclude that y varies directly with x.
To find the constant of variation (k), we need to choose any pair of x and y values and divide y by x:
Using the first pair (4, 6.4), k = 6.4 / 4 = 1.6.
Now we can write the equation for the direct variation:
y = kx
Substituting the value of k, the equation becomes:
y = 1.6x