one question plzzz helppppp
for the data in the table, does y vary directly with x? if it does, write an equation for the direct variation.
x , y
16 , 4
32 , 16
48 , 36
A: yes, y=2x
B: no, y does not vary directly with x
C: yes, y=8x
D: yes, y=4x
geez- could you not just try the choices?
A. clearly false, since 4 ≠ 2*16
same for C,D since clearly, y < x for all the values.
But, maybe it does vary directly, but it's not A,C,D.
Recall that direct variation means that y = kx for some constant k.
That means that y/x is constant
4/16 = 1/4
16/32 = 1/2
So clearly y/x is not constant. So pick B
To determine if y varies directly with x, we can check if the ratio of y to x remains constant for each pair of values. Let's calculate the ratios for the given data:
For the first pair (16, 4), the ratio is 4/16 = 1/4.
For the second pair (32, 16), the ratio is 16/32 = 1/2.
For the third pair (48, 36), the ratio is 36/48 = 3/4.
Since the ratios are not the same for each pair, y does not vary directly with x. Therefore, the correct answer is B: no, y does not vary directly with x.
To determine if y varies directly with x, we need to check if there is a constant ratio between the values of y and x.
In this case, we can calculate the ratio of y to x for each pair of values given in the table.
For the first pair, when x = 16, y = 4. So, y/x = 4/16 = 1/4.
For the second pair, when x = 32, y = 16. So, y/x = 16/32 = 1/2.
For the third pair, when x = 48, y = 36. So, y/x = 36/48 = 3/4.
Since the ratio y/x is not the same for all three pairs, we can conclude that y does not vary directly with x.
So the answer is B: no, y does not vary directly with x.