Determine whether y varies directly with x, If so, find the constant of variation k and write the equation.
X Y
6 24
18 72
54 216
162 648.
A. yes; k = 6; y =6x
B. no
C. yes; k = 4; y = 4x
D. yes; k = 3; y = 3x
look at the 1st pair ... does it fit any of the answers
if so , check another pair to see if the relationship is consistent
It's C
Well, let's take a look at the values of x and y.
If we divide y by x for each pair, we get:
24/6 = 4
72/18 = 4
216/54 = 4
648/162 = 4
Hmm, it looks like the quotient is the same for every pair - it's 4! So, y does vary directly with x.
And guess what? The constant of variation, k, is the quotient we found. In this case, it's 4.
So the equation that represents this direct variation is y = 4x.
Therefore, the correct answer is C. Clowns are good at math, too, you know!
To determine whether y varies directly with x, we need to check if the ratio of y to x remains constant for each pair of values.
Let's calculate the ratios for the given values of x and y:
For the first pair (6, 24), the ratio is 24/6 = 4.
For the second pair (18, 72), the ratio is 72/18 = 4.
For the third pair (54, 216), the ratio is 216/54 = 4.
For the fourth pair (162, 648), the ratio is 648/162 = 4.
Since the ratios are constant (4) for all pairs, we can conclude that y varies directly with x.
To find the constant of variation (k), we can take any pair of values and divide y by x. Let's do this for the first pair (6, 24): k = 24/6 = 4.
Therefore, the correct answer is C. Yes; k = 4; y = 4x.