Question

Tell whether each relationship is a direct variation. Explain your answer.

A. The equation y-2.00x = 2.50 relates the cost of y of a taxicab journey to distance X in km covered by the cab.

Answer= No, it cannot be written in the form of y = kx. Please, show the solution​

Answer 1

What Is Direct Variation?

There are many situations in our daily lives that involve direct variation.

For example, a worker may be paid according to the number of hours he worked. The two quantities x (the number of hours worked) and y (the amount paid) are related in such a way that when x changes, y changes proportionately such that the ratio remains a constant.

We say that y varies directly with x. Let us represent the constant by k, i.e.

or y = kx where k ≠ 0

If y varies directly as x, this relation is written as y ∝ x and read as y varies as x. The sign “ ∝ ” is read “varies as” and is called the sign of variation.

Example:

If y varies directly as x and given y = 9 when x = 5, find:

a) the equation connecting x and y

b) the value of y when x = 15

c) the value of x when y = 6

Solution:

a) y ∝ x i.e. y = kx where k is a constant

Substitute x = 5 and y = 9 into the equation:

y = x