Final answer:
All three options A, B, and C are linear equations because they can be written in the form y = mx + b, which describes a straight line. To simplify algebraic expressions, eliminate like terms and always verify your solutions for reasonableness.
Step-by-step explanation:
In the math subject of Algebra, you've asked which among the given equations are linear. A linear equation is any equation that can be written in the form y = mx + b, with m representing the slope and b representing the y-intercept. In Practice Test 4's 12.1 Linear Equations section, we are given the following options:
- A. y = -3x
- B. y = 0.2 +0.74x
- C. y=-9.4 - 2x
Each of these equations fits the linear equation form, so choices A, B, and C are correct. All three represent a straight line when graphed on a coordinate plane. To answer the question accurately, we use the concept that linear equations create straight lines, and any equation that can be reshaped into y = mx + b without changing its graph is considered linear.
To simplify the algebra, always combine like terms and reduce equations to their simplest form. Checking that the answer is reasonable involves making sure the solutions make sense in the context of the problem, including ensuring that you haven't introduced any extraneous solutions that don't satisfy the original equation.