Question

for each equation, determine whether it is linear.

equation	is the equation linear?
(a) $y = x + 9$	$\bigcirc$	$\bigcirc$
(b) $y = -2x^3$	$\bigcirc$	$\bigcirc$
(c) $y = x^2 + 6$	$\bigcirc$	$\bigcirc$
(d) $y = 4^x$	$\bigcirc$	$\bigcirc$

Explanation:

Part (a)

Step1: Recall linear equation form

A linear equation in two variables is of the form \( y = mx + b \), where \( m \) and \( b \) are constants, and the exponent of \( x \) is 1.

Step2: Analyze \( y = x + 9 \)

In \( y = x + 9 \), \( m = 1 \) and \( b = 9 \), and the exponent of \( x \) is 1. So it fits the linear equation form.

Step1: Recall linear equation form

A linear equation has \( x \) with exponent 1.

Step2: Analyze \( y = -2x^3 \)

Here, the exponent of \( x \) is 3, which is not 1. So it does not fit the linear equation form.

Step1: Recall linear equation form

Linear equations have \( x \) with exponent 1.

Step2: Analyze \( y = x^2 + 6 \)

The exponent of \( x \) is 2, not 1. So it is not linear.

Answer:

Yes

Part (b)