Question

Suppose y varies directly as x, and y = -65 when x = -26. Write a variation equation.

Answer 1

To write a variation equation when y varies directly as x, we need to find the constant of variation. Given that y = -65 when x = -26, we can plug these values into the direct variation equation and solve for the constant of variation. The variation equation is y = 2.5x.

Step-by-step explanation:

The given problem states that y varies directly as x. In a direct variation, as one variable increases or decreases, the other variable also increases or decreases in a proportional manner. To write a variation equation, we need to find the constant of variation (k).

Given that y = -65 when x = -26, we can plug these values into the direct variation equation: y = kx.

-65 = k(-26)

Now we can solve for k to find the variation equation.

k = -65 / -26 = 5/2 = 2.5

Therefore, the variation equation is y = 2.5x.