Tell whether y varies directly with x. If it does, write an equation for the direct variation.

Question

x: -1, 2, 5, 9
y: -6, 3, 12, 24

Answer 1

To determine if y varies directly with x, we need to check if the ratio of y to x remains constant for all pairs of values.

Let's calculate the ratios y/x for each pair:

-6 / -1 = 6
3 / 2 = 1.5
12 / 5 = 2.4
24 / 9 = 2.67

Since the ratios are not consistent, y does not vary directly with x. Therefore, we cannot write an equation for direct variation.

Answer 2

x: -3, -1, 2, 5
y: 7.5, 2.5, -5, -12.5

Answer 3

To determine if y varies directly with x in this case, we need to check if the ratio of y to x remains constant for all pairs of values.

Let's calculate the ratios y/x for each pair:

7.5 / -3 = -2.5
2.5 / -1 = -2.5
-5 / 2 = -2.5
-12.5 / 5 = -2.5

Since the ratios are consistent for all pairs, y varies directly with x. We can write the equation for direct variation as:

y = kx

To find the value of k, we can use any pair of x and y. Let's use x = -1 and y = 2.5:

2.5 = k(-1)

Solving for k, we get:

k = -2.5

Therefore, the equation for direct variation is:

y = -2.5x