Consider the function represented by the equation y-6x-9=0. Which answer shows the equation in a function notation with x as the independent variable

Solution:

The independent variable and dependent variable are on opposite sides of a function.

This is because we want to solve for the dependent variable when the independent variable is known.

We need to solve for y in the equation.

Add 6x and 9 on both sides of the equation.

y-6x-9+6x+9=6x+9

y=6x+9

y is the dependent variable and x is the independent variable.

The correct answer is f (x) = 6x + 9 or y = 6x + 9.

Step-by-step explanation:

Independent variable are those variables which can select constant values by itself.

Dependent Variable are those variables which are dependent on other variable of the equation.

Now, consider the provided equation y - 6x - 9 = 0.

We need to write the provided equation in a function notation with x as the independent variable and y will work as a dependent variable.

Therefore, add 6 x and 9 to both the sides of equation.

y - 6x - 9 + 6x + 9 = 6x + 9

y = 6x + 9

or

f (x) = 6x + 9

Hence, the correct answer is f (x) = 6x + 9 or y = 6x + 9.