Justify whether the equation y =9x-4

Question

defines a linear or nonlinear function.

Which statement is true?
The function is linear because the equation has the form
.
The function is linear because the equation contains only whole numbers.
The function is nonlinear because the equation does not have the form
.
The function is nonlinear because the equation contains only perfect squares.

Answer 1

To determine whether the equation \( y = 9x - 4 \) defines a linear or nonlinear function, we can analyze its form.

1. A linear function can be expressed in the standard form \( y = mx + b \), where \( m \) and \( b \) are constants. In this case, \( y = 9x - 4 \) fits this format, where \( m = 9 \) and \( b = -4 \).

2. The function is linear because the highest power of the variable \( x \) is 1. This indicates a straight line when graphed.

Now, let's evaluate each of the provided statements:

1. The function is linear because the equation has the form: This statement is true. The equation \( y = 9x - 4 \) is in the form of a linear equation.

2. The function is linear because the equation contains only whole numbers: This statement is false. The function can be linear regardless of whether it contains whole numbers or not.

3. The function is nonlinear because the equation does not have the form: This statement is false. The equation indeed has the correct linear form.

4. The function is nonlinear because the equation contains only perfect squares: This statement is false. The equation does not contain perfect squares; it is linear.

Therefore, the correct conclusion is that "The function is linear because the equation has the form \( y = mx + b \)."