Given that y varies directly with x in the table below, what is the value of y if the value of x is 7?
x
2
4
6
10
y
12
24
36
60
37
42
48
54
To find the value of y when x is 7, we need to determine the constant of variation between x and y. We can do this by finding the ratio of y to x for any pair of corresponding values. Let's choose the pair (2,12) from the table:
y/x = 12/2 = 6
So, the constant of variation is 6. Now we can use this constant to find the value of y when x is 7:
y = k * x
y = 6 * 7
y = 42
Therefore, the value of y when x is 7 is 42.
To determine the value of y when x is 7, we can use the concept of direct variation. This means that the ratio between x and y is constant.
From the given table, we can find the ratios between x and y:
2/12 = 4/24 = 6/36 = 10/60 = 37/222 = 42/252 = 48/288 = 54/324
We can observe that the ratio is approximately 1/6 in all cases:
2/12 ≈ 1/6
4/24 ≈ 1/6
6/36 ≈ 1/6
10/60 ≈ 1/6
37/222 ≈ 1/6
42/252 ≈ 1/6
48/288 ≈ 1/6
54/324 ≈ 1/6
Therefore, the value of y when x is 7 can be calculated as follows:
7/1 * 1/6 = 7/6
Hence, when x is 7, the value of y is approximately 7/6 or 1.17.