Question

Which of the following equations are linear?

a.) 3x + 5 = 0
b.) 6x² - 9 = 0
c.) 4x² - 8x + 9 - 3x² = x²
A. a) only
B. b) only
C. c) only
D. a) and c)

Answer 1

Only equation a.) 3x + 5 = 0 is a linear equation because it can be represented in the form y = mx + b, which is the standard form of a linear equation. The other options include quadratic terms, which means they are not linear equations.

Step-by-step explanation:

When identifying linear equations, we look for equations that can be written in the form y = mx + b, where m and b are constants, and x and y are variables. A linear equation represents a straight line when graphed on the Cartesian coordinate system.

In the question, we are asked which among the given equations are linear:

• a.) 3x + 5 = 0 is a linear equation because it can be rewritten as y = -3x - 5, which is of the form y = mx + b.

• b.) 6x² - 9 = 0 is not linear because it has the term x², making it a quadratic equation.

• c.) 4x² - 8x + 9 - 3x² = x² can be simplified to x² - 8x + 9 = 0, which is also not a linear equation as it contains the term x².

• Among the given options, only equation a is linear. Therefore, the correct answer is A. a) only.