Question

Given that y is inversely as x+3 and that y=4 when x =2 (a)express y in terms of x (b)find the value of y when x =5 .

Answer 1

a. Expressing y in terms of x, y = 20/(x + 3)

b. When x = 5, the value of y is 2.5

The question has to do with inverse variation.

What is inverse variation?

Inverse variation is variation in which one quantity varies inversely as the other.

a. How to express y in terms of x?

Given that y is inversely as x + 3 and that y = 4 when x = 2.

Since y varies inversely as x + 3, we have

y ∝ 1/(x + 3)

y = k/(x + 3)

When y = 4, x = 3. So

y = k/(x + 3)

4 = k/(2 + 3)

4 = k/5

k = 4 × 5

k = 20

So, y = k/(x + 3)

y = 20/(x + 3)

So, expressing y in terms of x, y = 20/(x + 3)

b. Find the value of y when x = 5.

Since  y = 20/(x + 3)

Substituting x = 5 into the equation, we have

y = 20/(x + 3)

y = 20/(5 + 3)

y = 20/8

y = 5/2

y = 2.5

So, when x = 5, the value of y is 2.5

Learn more about inverse variation here:

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