If y y varies directly as x x , and y = 18 y=18 when x = 6 x=6 , find y y when x = 10 x=10 .

this problem, we have that y varies directly as x, and we have that y equals 18 when x equals six. We're asked to find y when x is equal to 10. Now to solve this problem, our first step is going to be set up the setting up the equation that relates y and x. Now I know for a direct relationship, for direct variation, we have that y is equal to k times x. Now you can see at one moment, y is equal to 18, and at that same moment, x is equal to six. So what I need to do is go ahead and solve for my constant k by dividing the six on both sides of the equal sign. That'll get the sixes to cancel leaving me with just k. And 18 divided by six, well that comes out to three. So we now have the k value that we're looking for, which means I can rewrite my equation. I can write that y is equal to our k value of three times x. So we don't have the linear equation that relates y and x. And now what I can do is solve the problem that tells me to find y when x is equal to 10. So that means I just need to go into this equation, and I need to replace my x with 10. And three times 10 comes out to 30, so that right there would be the answer to this problem.

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Multiple Choice

If $y$ varies directly as $x$ , and $y equals 18$ when $x equals 6$ , find $y$ when $x equals 10$ .

$3$

$30$

$60$

$9$

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If $y$ varies directly as $x$ , and $y equals 18$ when $x equals 6$ , find $y$ when $x equals 10$ .