Chapter 8, Problem 4MCQ

Solution

To identify: The relationship between the values in the table is a direct variation, inverse variation or neither.

x	22	35	48	54
y	104	174	239	269

The relationship between the variables is neither.

Given information:

The given table is:

x	22	35	48	54
y	104	174	239	269

Explanation:

If the two variables $x\text{and}y$ are in direct variation then $y=kx\text{or}\frac{y}{x}=k$ .

If the two variables $x\text{and}y$ are in inverse variation then $xy=k$ , where k is the constant of variation.

Now observe the given table:

  $\begin{array}{c}22\cdot 104=2288\\ 35\cdot 174=6090\\ 48\cdot 239=11472\\ 54\cdot 269=14526\end{array}$

It can be seen that $xy$ is not a constant because the product of each pair in the table is not same.

Now find $\frac{y}{x}$ for each pair,

  $\begin{array}{c}\frac{104}{22}\approx 4.727\\ \frac{174}{35}\approx 4.971\\ \frac{239}{48}\approx 4.979\\ \frac{269}{54}\approx 4.981\end{array}$

It can be seen that $\frac{y}{x}$ is not a constant because the ratio of each pair in the table is not same. So the variables are not in direct variation.

Therefore, the relationship between the variables is neither direct variation nor inverse variation.