Question

X Y-2 -4-4 -8-16 -32Does y varies directly with x If so find the constant of variation AND write the equation

Answer 1

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:

`\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:} \\ (-4)/(-2)\text{ = k} \\ k\text{ =2} \\ \text{Hence, the equation is given as :} \\ Y\text{ = 2 X} \end{gathered}`