Respuesta :

iGreen
7.

Direct variation is:

[tex]\sf y=kx[/tex]

Where 'k' is the constant of variation. Let's plug in y = -6 and x = 10 into the formula:

[tex]\sf -6=k(10)[/tex]

Divide 10 to both sides:

[tex]\sf k=-\dfrac{3}{5}[/tex]

Plug this in for 'k' in our formula:

[tex]\sf y=-\dfrac{3}{5}x[/tex]

This is our formula. To find out what 'y' is when 'x' = 5, plug in 5 for 'x':

[tex]\sf y=-\dfrac{3}{5}(5)[/tex]

Multiply:

[tex]\boxed{\sf y=-3}[/tex]

9.

Let's plug in y = 9 and x = 8 into our formula:

[tex]\sf 9=k(8)[/tex]

Divide 8 to both sides:

[tex]\sf k=\dfrac{9}{8}[/tex]

So our equation is:

[tex]\sf y=\dfrac{9}{8}x[/tex]

Now let's plug in 18 for 'y' to find out what 'x' is when y = 18:

[tex]\sf 18=\dfrac{9}{8}x[/tex]

Divide 9/8 to both sides or multiply by its reciprocal 8/9:

[tex]\sf x=18\cdot\dfrac{8}{9}\rightarrow \boxed{\sf 16}[/tex]

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