determine whether y varies directly with x .if so , find the constant of varition k and write the equation
x :7
y:14
x :18
y:16
x:9
y:15
x:10
y:17
show all work
In order to determine whether y varies directly with x, we need to check if the ratio of y to x is constant for all given values of x and y.
For the first set of values:
x = 7, y = 14
The ratio of y to x is 14/7 = 2.
For the second set of values:
x = 18, y = 16
The ratio of y to x is 16/18 = 8/9.
Since the ratios for the first two sets of values are not the same, we can conclude that y does not vary directly with x.
However, let's check the remaining two sets of values for confirmation:
For the third set of values:
x = 9, y = 15
The ratio of y to x is 15/9 = 5/3.
For the fourth set of values:
x = 10, y = 17
The ratio of y to x is 17/10.
Since the ratios for the third and fourth sets of values are also different from each other, we can confirm that y does not vary directly with x.
Therefore, we cannot find the constant of variation (k) or write an equation for y in terms of x as y = kx.