Question

Determine whether y varies directly with x. If so, find the constant of variation and write the equation.

yes; k = −4 and x = −4y
yes; k = −4 and y = −4x
yes; k = 4 and y = 4x
No

Answer 1

Answer: Third Option

yes; k = 4 and y = 4x

Explanation:

Observe in the values of x and y given that when x decreases the variable-y also decreases.

Then the variation is direct.

Then, if between any two points of the function, the rate of variation k remains the same then the variation is constant.

We can test whether these conditions are met by using the given points.

(-2, -8) and (-4, -16)

The rate of variation k for these points is:

`k = (y_2-y_1)/(x_2-x_1)\\\\k =(-16-(-8))/(-4-(-2))\\\\k = (-16+8)/(-4+2)\\\\k =4`

Now we calculate the variation rate for the points

(-4, -16) and (-6, -24)

`k = (y_2-y_1)/(x_2-x_1)\\\\k =(-24-(-16))/(-6-(-4))\\\\k = (-24+16)/(-6+4)\\\\k =4`

The rate of variation is constant and equal to 4.

Then the answer is yes; k = 4 and y = 4x