Question

for each equation, determine whether it is linear.

equation	is the equation linear?
(a) $y = 1$	$\circ$	$\circ$
(b) $y = -4x^2 + 3$	$\circ$	$\circ$
(c) $y = 7x + 1$	$\circ$	$\circ$
(d) $y = -x$	$\circ$	$\circ$

Explanation:

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 highest power of \( x \) is 1.

Step2: Analyze equation (a) \( y = 1 \)

Rewrite as \( y = 0x + 1 \). Here, \( m = 0 \), \( b = 1 \), highest power of \( x \) is 1. So linear (Yes).

Step3: Analyze equation (b) \( y = -4x^2 + 3 \)

Highest power of \( x \) is 2, which is not 1. So not linear (No).

Step4: Analyze equation (c) \( y = 7x + 1 \)

In form \( y = mx + b \) with \( m = 7 \), \( b = 1 \), highest power of \( x \) is 1. So linear (Yes).

Step5: Analyze equation (d) \( y = -x \)

Rewrite as \( y = -1x + 0 \), \( m = -1 \), \( b = 0 \), highest power of \( x \) is 1. So linear (Yes).

Answer:

(a) Yes
(b) No
(c) Yes
(d) Yes

(For each equation, mark the corresponding "Yes" or "No" circle. Specifically:

• (a): Mark "Yes"
• (b): Mark "No"
• (c): Mark "Yes"
• (d): Mark "Yes")