Question

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Answer 1

Answer:

Yes, y varies directly with x, and the equation is $y=1.6x$.

Step-by-step explanation:

To check where there is a direct relationship between x and y, we need to check whether all the x,y pairs we have fit some rule:

$y=k\times x$.

For the first pair (x=4, y=6.4),

$6.4=k\times 4$

Therefore $k = 1.6$.

For the second pair (x=7, y=11.2),

$11.2=k\times 7$

Therefore $k = 1.6$.

For the third pair (x=10, y=16),

$16=k\times 10$

Therefore $k = 1.6$.

For the second pair (x=13, y=20.8),

$20.8=k\times 13$

Therefore $k = 1.6$.

So x does directly vary with y, and we have found out that $k=1.6$.

Answer 2

Answer:   $\bold{\dfrac{y}{x}=1.6\quad \text{which is also equivalent to}\quad y=1.6x}$

Step-by-step explanation:

$\begin {array}{c|c||l}x&y&\dfrac{y}{x}=k\\--&--&-----\\4&6.4&\dfrac{6.4}{4}=1.6\\\\11.2&7&\dfrac{11.2}{7}=1.6\\\\10&16&\dfrac{16}{10}=1.6\\\\13&20.8&\dfrac{20.8}{13}=1.6\\\end{array}$

Since the k-value is the same for every value in the table, we can conclude that y varies directly with x and the constant of variation k = 1.6