Question

Can someone plz help me thank you

Answer 1

7.

Direct variation is:

$\sf y=kx$

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

$\sf -6=k(10)$

Divide 10 to both sides:

$\sf k=-\dfrac{3}{5}$

Plug this in for 'k' in our formula:

$\sf y=-\dfrac{3}{5}x$

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

$\sf y=-\dfrac{3}{5}(5)$

Multiply:

$\boxed{\sf y=-3}$

9.

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

$\sf 9=k(8)$

Divide 8 to both sides:

$\sf k=\dfrac{9}{8}$

So our equation is:

$\sf y=\dfrac{9}{8}x$

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

$\sf 18=\dfrac{9}{8}x$

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

$\sf x=18\cdot\dfrac{8}{9}\rightarrow \boxed{\sf 16}$