Final answer:
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.