Chapter E, Problem 1ES

Write a direct variation equation, $y=kx$, that satisfies the ordered pairs in each table. See Example 1.

To determine

To write a direct variation equation for the ordered pairs given in the table below:

x	0	6	10
y	0	3	5

Answer to Problem 1ES

  $y=\frac{1}{2}x$.

Explanation of Solution

Given Information:

The table is given below:

x	0	6	10
y	0	3	5

Formula used:

A direct variation equation is given by $y=kx$ , where k is the constant.

Calculation:

A direct variation equation is $y=kx$.

Substitute the ordered pair $\left(6,3\right)$ in the above equation, to get,

  $\begin{array}{c}3=k\left(6\right)\\ k=\frac{3}{6}\\ =\frac{1}{2}\end{array}$

Hence, the required direct variation equation is $y=\frac{1}{2}x$.