To determine if y varies directly with x, we need to check if the ratio of y to x is constant for all the given values. Let's calculate the ratio for each pair of values:
For the first pair (x = 4, y = 6):
y/x = 6/4 = 1.5
For the second pair (x = 7, y = 10.5):
y/x = 10.5/7 = 1.5
For the third pair (x = 10, y = 15):
y/x = 15/10 = 1.5
For the fourth pair (x = 13, y = 19.5):
y/x = 19.5/13 = 1.5
Since the ratio of y to x is constant (1.5) for all the values, we can conclude that y varies directly with x.
To find the constant of variation (k), we can choose any pair of values and calculate the ratio again. Let's choose the first pair:
k = y/x = 6/4 = 1.5
Therefore, the constant of variation (k) is 1.5.
The equation for direct variation between x and y is y = kx. Substituting the value of k:
y = 1.5x
x:4, 7, 10, 13
y:6, 10.5, 15, 19.5
determine whether y varies directly with x if so find the constant of variation k and write the equation
1 answer