Math Problem Statement

If y varies directly as x, and y = 7 when x = 6, find y when x = 18.

Solution

The problem states that "y varies directly as x," meaning that there is a direct proportional relationship between yy and xx, which can be expressed as:

y=kxy = kx

where kk is the constant of proportionality.

We are given that y=7y = 7 when x=6x = 6. Let's use this to find kk:

7=k×67 = k \times 6 k=76k = \frac{7}{6}

Now that we have kk, we can find yy when x=18x = 18:

y=76×18=21y = \frac{7}{6} \times 18 = 21

So, when x=18x = 18, y=21y = 21.

Do you need more details on any part of the explanation? Here are five related questions to expand your understanding:

  1. What is the difference between direct and inverse variation?
  2. Can you express direct variation as a ratio between two variables?
  3. How would you find xx if you were given yy and the constant kk?
  4. What happens to yy if xx is doubled in a direct variation?
  5. How can you graph a direct variation equation like this one?

Tip: In a direct variation, as one variable increases, the other increases proportionally, and the ratio between them remains constant.

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Math Problem Analysis

Mathematical Concepts

Direct Proportionality
Algebra

Formulas

y = kx

Theorems

Direct Variation Theorem

Suitable Grade Level

Grades 7-9