Question

Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.

Answer 1

You can either use the slope formula, \[m = \frac{ y _{2}-y _{1} }{ x _{2}-x _{1} }\] or more simply, because it's only of the form y = mx, just divide each y term by it's x term, and check they all give the same value

ie

24/6 =
72/18 =
216/54 =
648/162 =

Check they all equal the same number.

Answer 2

they all equal 4 @agent0smith

Answer 3

Which means each x is multiplied by 4 to get y, so the constant of variation is 4

Answer 4

hmm. ok so how would i know which answer is right?

yes; k = 4; y = 4x
yes; k = 3; y = 3x
yes; k = 6; y = 6x
no

Answer 5

i think that no is not the right answer @agent0smith

Answer 6

note that k is the constant of variation, and the constant of variation is 4 from what you worked out above.

Answer 7

so A! @agent0smith

Answer 8

Correct :)

Answer 9

thank you so much @agent0smith i really appreciate it <3

Answer 10

No prob :)