Final answer:
To determine if an equation is a linear equation in two variables, look for an equation of the form y = mx + b, where 'm' and 'b' are constants and the variables 'x' and 'y' are raised to the power of 1, such as equations A, B, and C from the practice test.
Step-by-step explanation:
To determine if an equation is a linear equation in two variables, you should look for an equation of the form y = mx + b, where 'm' and 'b' are constants, and the variables 'x' and 'y' are raised to the power of 1. Answering the student's question directly, option D is correct: Linear equations have variables raised to the power of 1.
Looking at the provided options for linear equations, equations
A (y = -3x), B (y = 0.2 + 0.74x), and C (y = -9.4 - 2x) are all in the form of a linear equation, which is y = a + bx, with 'a' as the y-intercept and 'b' as the slope. Therefore, the correct answer to the practice test question is E: A, B, and C.
In linear equations, it's also important to identify the independent variable and the dependent variable. The independent variable is the variable that is being manipulated or changed, usually represented as 'x', while the dependent variable is the one being measured or affected by the independent variable, usually represented as 'y'.