x y
4 6.4
7 11.2
10 16
13 20.8
Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.
To determine whether y varies directly with x, we can check if the ratios of y and x are always the same. We can calculate the ratios for the given values of x and y:
For the first pair (x=4, y=6.4), the ratio is 6.4/4 = 1.6.
For the second pair (x=7, y=11.2), the ratio is 11.2/7 = 1.6.
For the third pair (x=10, y=16), the ratio is 16/10 = 1.6.
For the fourth pair (x=13, y=20.8), the ratio is 20.8/13 = 1.6.
Since the ratios are always the same (1.6), this indicates that y varies directly with x.
To find the constant of variation (k), we can pick any pair of x and y and divide them to get the ratio. Let's take the first pair:
k = y/x = 6.4/4 = 1.6
So the equation of variation is y = kx, which can be written as y = 1.6x.
show steps without explaining
Step 1: Calculate the ratios of y and x for each pair of values.
- Ratio 1: 6.4/4 = 1.6
- Ratio 2: 11.2/7 = 1.6
- Ratio 3: 16/10 = 1.6
- Ratio 4: 20.8/13 = 1.6
Step 2: Since the ratios are always the same (1.6), y varies directly with x.
Step 3: Calculate the constant of variation (k) using any pair of x and y.
- k = 6.4/4 = 1.6
Step 4: Write the equation of variation.
- y = kx
- y = 1.6x