enter your answer and show all the stop that you use to solve this problem in the space provided determine whether y varies directly with x if so find the constant of varation k write the equation x 7 8 9 10 y 14 16 15 17
To determine whether y varies directly with x, we need to check if the ratio of y to x is constant. Let's find this ratio for each pair of values:
For (7, 14): 14/7 = 2
For (8, 16): 16/8 = 2
For (9, 15): 15/9 = 1.67
For (10, 17): 17/10 = 1.7
Since the ratios are not the same for all pairs of values, y does not vary directly with x.
Therefore, we cannot find a constant of variation k or write an equation in the form y = kx.
To determine whether y varies directly with x, we can use the given data to check if the ratios of y to x remain constant. If they do, then y varies directly with x.
Let's calculate the ratios for the given data points:
Ratio 1: y/x = 14/7 = 2
Ratio 2: y/x = 16/8 = 2
Ratio 3: y/x = 15/9 ≈ 1.67
Ratio 4: y/x = 17/10 ≈ 1.7
Since the ratios are not constant, y does not vary directly with x.
Therefore, we cannot find a constant of variation (k) or form a direct variation equation for this data set.
To determine whether y varies directly with x, we need to check if there is a constant ratio between the values of y and x. If there is a constant ratio, it means y varies directly with x.
To find the constant of variation (k), which indicates this constant ratio, we can choose any two pairs of x and y values and use the following formula:
k = y / x
Let's choose the pairs (7,14) and (10,17):
For the first pair (7,14):
k = 14 / 7 = 2
For the second pair (10,17):
k = 17 / 10 = 1.7
Since the two results are not equal, there is no constant ratio between the values of y and x. Therefore, we can conclude that y does not vary directly with x.
To write the equation for direct variation, we use the formula:
y = kx
As we have determined that there is no direct variation between y and x, we cannot write an equation for direct variation in this case.