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

Solution:

The table below depicts a relationship described by the expression xy = k.

xy = k only if

x ∝ 1/y

From the table we find,

xy = 0.002 × 500 = 0.004 × 250 = 0.008 × 125 = 0.06 × 62.5 = 0.05 × 31.25 = 1 = k

Hence x and y are inversely proportional to each other.

✦ Try This: Establish the type of proportionality between the variables p and q.

To establish the type of proportionality between the two variables we have to ascertain one of the two types given below:

1) x ∝ 1/y

2) x ∝ y

If x ∝ y, then

x/y = k where k is a +ve proportionality constant

x/y = 1/7 = 2/14 = 3/21 = 4/28 = 5/35 = 1/7 = k

If x ∝ 1/y, then

xy = 1 × 7 ≠ 2 × 14 ≠ 3 × 21 ≠ 4 × 28 ≠ 5 × 35 ≠ k

Hence we can conclude that x and y are directly proportional.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 13

NCERT Exemplar Class 8 Maths Chapter 10 Problem 21

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

Summary:

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

☛ Related Questions:

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