Question

The variables x and y vary directly. Use the given values of the variables to write an equation that relates x and y x=-2, y=-2

Answer 1

Please check the explanation.

Explanation:

We know that when y varies directly with x, we get the equation

y ∝ x

y = kx

k = y/x

where 'k' is called the 'constant of direct variation'.

We are given that x = -2 and y = -2

Thus,

The equation is:

y = kx

substituting x = -2 and y = -2

-2 = k(-2)

-2 = -2k

We can further simplify the equation to determine the value of 'k'

so

dividing the equation by -2

-2/-2 = -2k/-2

1 = k

Therefore, the value of k = 1

Thus, the equation becomes

y = kx

substituting k = 1 in the equation

y = (1)x

y = x

Therefore, an equation that relates x and y is:

y = x