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4. If y varies directly as x and y = -18 when x = 9, find y when x = 7.

M) 7
A) -7
T-14
H) 14​

Sagot :

DIRECT VARIATION

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MATHEMATICAL STATEMENT:

  • y varies directly as x

EQUATION:

  • y = kx

where k is the constant of the variation

GIVEN:

  • y = - 18 when x = 9

UNKNOWN:

  • constant of the variation k
  • y when x = 7

SOLUTION:

First we have to find the value of k using the given values.

[tex] \tt y = kx \\ \\ \tt - 18 = k(9) \\ \\ \tt - 18 = 9k \\ \\ \tt \frac{ - 18}{9} = \frac{9k}{9} \\ \\ \boxed{ \tt k = - 2}[/tex]

Now that we have the value of k, we can already find y when x = 7

[tex] \tt y = kx \\ \\ \tt y = ( - 2)(7) \\ \\ \tt \boxed{ \red{ \tt y= - 14}}[/tex]

∴ y = - 14 when x = 7

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