Question

FAN AND MEDAL!!!

Answer 1

What is the constant of variation in the graph below?

A graph is shown that has the following points plotted: two comma thirty-six, three comma twenty-four, four comma eighteen, and six comma twelve.

seventy-two

thirty-six

eighteen

8

Answer 2

Hey...I'll take a look!

Answer 3

k thanks

Answer 4

ok

Answer 5

I am having a difficult time with this one. The constant of variation is another phrase for "slope". But when you graph those points you do not get a straight line, it is curved. Therefore the constant of variation is never the same between two points. Let me look into this further for a tiny bit.

Answer 6

Oh duh. I'm sorry...brain lapse. This is curved because it is indirect variation. That formula is

Answer 7

\[y=\frac{ k }{ x }\]

Answer 8

Taking each of your given points and subbing in the x and the y you find k to be the same each time. Here:\[y=\frac{ k }{ x }->36=\frac{ k }{ 2 }\]Solving for k you get 72, which is the constant of variation. Let's do another so you can see that it is true.

Answer 9

ok

Answer 10

Using the point (3, 24)\[24=\frac{ k }{ 3 }\]Solving for k gives you k = 72. Same as above. Right?

Answer 11

yup

Answer 12

(4, 18):\[18=\frac{ k }{ 4 }\]k = 72. Yay! The constant of variation is 72.

Answer 13

You could even use that k value to find the missing (5, y) value in your list.\[y=\frac{ 72 }{ 5 }\]y = 14.4 Which is probably why they didn't give it to you to graph. But there it is!