Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.
The table ges right side dwnards, 7,8,9,10
the left side dwn ges 11, 13, 15, 17
Now I understand it I just don't knw how t write it. Help please
obviously not direct variation. If x=in and y=out, it is clear that y changes by 2 when x changes by 1, so
y = 2x + some offset.
Looking at x=7, we see that
y = 2x - 3
To determine whether y varies directly with x, we need to check if the ratio between the variables remains constant.
Let's use the given table of values:
x: 7, 8, 9, 10
y: 11, 13, 15, 17
To find out if y varies directly with x, we can compare the ratios of the corresponding values of x and y. If the ratios are equal, then y varies directly with x.
Let's calculate the ratios for each pair of values:
For the first pair (7, 11):
Ratio = y/x = 11/7 ≈ 1.57
For the second pair (8, 13):
Ratio = y/x = 13/8 ≈ 1.62
For the third pair (9, 15):
Ratio = y/x = 15/9 ≈ 1.67
For the fourth pair (10, 17):
Ratio = y/x = 17/10 ≈ 1.7
Since the ratios are approximately equal, we can conclude that y varies directly with x.
To find the constant of variation (k) and write the equation, we can use the formula for direct variation, which is:
y = kx
To find k, we can choose any pair of x and y values. Let's use the first pair (7, 11):
11 = k * 7
Solving for k:
k = 11/7 ≈ 1.57
Now we can write the equation:
y = 1.57x