Question

Which explains whether or not the values in the table represent a direct variation? x 4 6 10 20 y 1 1.5 2.5 5 The table represents a direct variation because the values are proportional. The table represents a direct variation because the values are nonproportional. The table does not represent a direct variation because the values are proportional. The table does not represent a direct variation because the values are nonproportional.

Answer 1

Answer:

Option A is correct.

The table represents a direct variation because the values are proportional.

Step-by-step explanation:

The direct variation says that:

$y \propto x$

then; the equation is of the form : $y =kx$ where k is the Constant of Variation.

Consider any values of x and y from the table, to solve for k;

Let x = 10 and y = 2.5

then;

$2.5 = 10k$

Divide both sides by 10 we have;

$k = \frac{2.5}{10} = \frac{25}{100} = \frac{1}{4}$

Then the equation becomes:

$y =\frac{1}{4}x$

Therefore, the table represents a direct variation because the values are proportional.

Answer 2

Answer: A The table represents a direct variation because the values are proportional.

Step-by-step explanation: