x:7,8,9,10
y:14,16,15,17
determine whether y varies directly with x if so find the constant of variation k and wrte the equation
To determine whether y varies directly with x, we need to check if the ratio of y to x is constant. Let's find the ratio for each pair of corresponding values:
For (x=7, y=14): y/x = 14/7 = 2
For (x=8, y=16): y/x = 16/8 = 2
For (x=9, y=15): y/x = 15/9 = 5/3
For (x=10, y=17): y/x = 17/10 = 1.7
Since the ratios are not constant, y does not vary directly with x.
Therefore, we cannot find the constant of variation (k) and write the equation for this situation.
To determine whether y varies directly with x, we need to check if the ratio of y to x is constant for all values. Let's calculate the ratios:
Ratio 1 = y1/x1 = 14/7 = 2
Ratio 2 = y2/x2 = 16/8 = 2
Ratio 3 = y3/x3 = 15/9 = 1.67
Ratio 4 = y4/x4 = 17/10 = 1.7
As we can see, the ratios are not the same for all values. Therefore, y does not vary directly with x.
If y did vary directly with x, the ratio would be constant, and we could find the constant of variation (k) by calculating any of the ratios.
Let's take the ratio from the first pair of values:
k = y1/x1 = 14/7 = 2
So, if y varied directly with x, the equation would be: y = 2x
To determine if y varies directly with x, we can check if the ratios of corresponding values of x and y are equal.
Given:
x: 7, 8, 9, 10
y: 14, 16, 15, 17
Let's calculate the ratios of corresponding x and y values:
Ratio1 = y1 / x1 = 14 / 7 = 2
Ratio2 = y2 / x2 = 16 / 8 = 2
Ratio3 = y3 / x3 = 15 / 9 ≈ 1.67
Ratio4 = y4 / x4 = 17 / 10 = 1.7
Since the ratios are not equal for all values, y does not vary directly with x.
If the ratios were equal, we could find the constant of variation (k) by taking the ratio of any x and y value. In this case, there is no constant of variation and the equation for direct variation cannot be written.