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Chapter 3: Q15. (page 205)

Suppose yvaries directly as x. Write a direct variation equation that relates x and y. Then solve.

Ify=6 when x=9, find x when y=12.

Short Answer

Expert verified

The direct variation equation that relates x and y isy=23x and the value of x wheny=12 is 18.

Step by step solution

01

Step 1. Write a direct variation equation that relates x and y.

It is given that y varies directly as x.

Therefore it implies that y伪x.

Therefore, it is obtained that:

y伪xy=kx

Where is k constant of proportionality.

It is given that when x=9,y=6.

Therefore, substitute 9 for x and 6 for y in the equationy=kx to find the value of k.

y=kx6=k969=k23=k

Substitute the value of k in the equation y=kx.

Therefore, it is obtained that:

y=kxy=23x

Therefore, the direct variation equation that relates x and y is y=23x.

02

Step 2. Find the value of x when y=12.

The direct variation equation that relates x and y is y=23x.

Find the value of x by substituting 12 for y in the equation y=23x.

y=23x12=23x12脳3=2x36=2x362=x18=x

Therefore, the value of x wheny=12 is 18.

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