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Chapter 3: Q16. (page 206)

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

When y=鈭�8, x=8. What is x when y=鈭�6?

Short Answer

Expert verified

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

The value of x wheny=鈭�6 is 6.

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 k is constant of proportionality.

It is given that when y=鈭�8,x=8.

Therefore, substitute -8 for y and 8 for x in the equation y=kxto find the value of k.

y=kx鈭�8=k8鈭�88=k鈭�1=k

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

Therefore, it is obtained that:

y=kxy=鈭�1xy=鈭�x

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

02

Step 2. Find the value of x when y=−6.

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

Find the value of x by substituting-6 for y in the equation y=鈭�x.

y=鈭�x鈭�6=鈭�x6=x

Therefore, the value of x wheny=鈭�6 is 6.

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Most popular questions from this chapter

Graph each equation.

2x鈭�3y=6

State whether each sentence is true or false. If false replace the underlined word or number to make a true sentence.

The regular form of a linear equation isAx+By=C.

Find the slope of the line that passes through each pair of points.

6,鈭�3,6,4

Sean鈥檚 class is selling boxes of popcorn to raise money for a class trip. Sean鈥檚 class paid \(85 for the popcorn, and they are selling each box for \)1. The functiony=x鈭�85 represents their profit y for each box of popcorn sold x. Find the zero and describe what it means in this situation.

Find the slope of the line that passes through each pair of points.

5,鈭�2,3,鈭�2
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