x y
7 11
8 13
9 15
10 17
Determine whether y varies directly with c. if so, find the constant of the variation k and write the equation
To determine if y varies directly with c, we need to check if the ratios of y to c are constant. Let's calculate the ratios for each pair:
For the first pair (x=7, y=11), the ratio of y to c is 11/7 = 1.57.
For the second pair (x=8, y=13), the ratio of y to c is 13/8 = 1.625.
For the third pair (x=9, y=15), the ratio of y to c is 15/9 ≈ 1.67.
For the fourth pair (x=10, y=17), the ratio of y to c is 17/10 = 1.7.
Since the ratios are not constant, y does not vary directly with c. Therefore, we cannot find a constant of variation (k) or write an equation for the relationship between y and c.
To determine whether y varies directly with x, we need to check if the ratio of y to x remains constant. Let's calculate the ratios for the given data:
Ratio for the first set of data (7, 11):
y / x = 11 / 7 = 1.571
Ratio for the second set of data (8, 13):
y / x = 13 / 8 = 1.625
Ratio for the third set of data (9, 15):
y / x = 15 / 9 = 1.667
Ratio for the fourth set of data (10, 17):
y / x = 17 / 10 = 1.7
Since the ratios are not the same for all the data sets, y does not vary directly with x.
Therefore, there is no constant of variation (k) and there is no equation that describes the relationship between y and x.
To determine if y varies directly with x, we need to check if the ratio of y to x remains constant for all the given data points. If the ratio remains constant, we can conclude that y varies directly with x.
Let's find the ratio of y to x for each data point:
For the first data point (x=7, y=11): y/x = 11/7 = 1.57
For the second data point (x=8, y=13): y/x = 13/8 = 1.625
For the third data point (x=9, y=15): y/x = 15/9 = 1.67
For the fourth data point (x=10, y=17): y/x = 17/10 = 1.7
As we can see, the ratio of y to x is not remaining constant. It is changing slightly for each data point. Therefore, we can conclude that y does not vary directly with x.
If y had varied directly with x, the ratio y/x would have remained constant. To find the constant of the variation (k), we can take any ratio y/x and use it to form an equation of the form y = kx. However, since we already determined that y does not vary directly with x, we cannot find the constant of the variation or write the equation.