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.

Option A is correct.

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

Step-by-step explanation:

The direct variation says that:

then; the equation is of the form : 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;

Divide both sides by 10 we have;

Then the equation becomes:

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

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

Step-by-step explanation:

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .