SOLUTION:
Step 1:
In this question, we are given the following:
X Y
-2 -4
-4 -8
-16 -32
a) Does y varies directly with x?
b) If so find the constant of variation and write the equation
Step 2:
From the table, we can see that:
when x = -2, y = -4,
when x = -4, y = -8,
when x = -16, y =-32.
We can see that there is a constant multiplication of 2,
This means that y varies directly with x
Step 3:
Part B:
From step 2, we can see clearly that the constant of variation, k = 2.
Then the equation is given as:
[tex]\begin{gathered} Given\text{ } \\ Y\text{ }\alpha\text{ X} \\ Y\text{ = k X} \\ \text{when X = -2, Y = -4, we have that:} \\ -4\text{= k ( -2)} \\ Divide\text{ both sides by -2, we have that:} \\ \frac{-4}{-2}\text{ = k} \\ k\text{ =2} \\ \text{Hence, the equation is given as :} \\ Y\text{ = 2 X} \end{gathered}[/tex]