# x and y are said to vary directly with each other if for some positive number k, ______ = k

**Solution**:

Consider the following table showing the direct relationship between two variables x and y.

x |
1 |
2 |
3 |
4 |
5 |

y |
3 |
6 |
9 |
12 |
15 |

Let us investigate the relationship x/y by using all the table values of x and y

x/y = 1/3 = 2/6 = 3/9 = 4/12 = 5/15 = 1/3 = k

Since k is a constant we can state that there exists a relationship between variable x and y which is of direct proportion. In other words x and y vary directly

Hence we see that the relationship between x and y is of direct variation.As x increases, y also increases.

**Summary:**

x and y are said to vary directly with each other if for some positive number k, __x/y __= k

**Try This: **Identify the relationship between the variables x and y from the values given in the table below:

x |
1/6 |
1/12 |
1/18 |
1/14 |
1/16 |

y |
1/3 |
1/6 |
1/9 |
1/7 |
1/8 |

Let us assume that xy = k

xy = 1/6 × 1/3 ≠1/12 × 1/6 ≠ 1/18 × 1/9 ≠ 1/14 × 1/7 ≠ 1/16 ×1/8 ≠ k

Hence the relationship between the variables is __not inverse__ in nature

Let us assume x/y = k

x/y = 1/6/(1/3) = 1/12/(1/6) = 1/18/(1/9) = 1/14/(1/7) = 1/16/(1/8)=1/2 = k

Hence the variables are varying directly with each other.

**ā Also Check: **NCERT Solutions for Class 8 Maths Chapter 13

**NCERT Exemplar Class 8 Maths Chapter 10 Problem 22**

## x and y are said to vary directly with each other if for some positive number k, x/y= k

**Summary**:

x and y are said to vary directly with each other if for some positive number k, ** xy** =k

**ā Related Questions:**

- Two quantities are said to vary ______ with each other if they increase (decrease) together in such . . . .
- Two quantities are said to vary ______ with each other if an increase in one causes a decrease in t . . . .
- If 12 pumps can empty a reservoir in 20 hours, then time required by 45 such pumps to empty the same . . . .

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