1. For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation.

Question

x - y:
8 - 13
16 - 26
24 - 39

Answer 1

To determine if y varies directly with x, we need to determine if there is a constant ratio between the two variables. To do this, we can calculate the ratio of y to x for each pair of values in the table:

For the first pair (8, 13), the ratio is 13/8 = 1.625.
For the second pair (16, 26), the ratio is 26/16 = 1.625.
For the third pair (24, 39), the ratio is 39/24 = 1.625.

Since the ratio is the same for all pairs, we can conclude that y varies directly with x.

To write an equation for the direct variation, we can use the form y = kx, where k is the constant of variation.

Since the ratio for all pairs is 1.625, we can use this value for k.

Therefore, the equation for the direct variation is:

y = 1.625x