Final answer:
To determine if two lines are parallel or perpendicular, one must analyze their slopes. Parallel lines have identical slopes, while perpendicular lines have slopes which are negative reciprocals of each other. Linear equations are presented in the form y = mx + b, where m is the slope and b is the y-intercept.
Step-by-step explanation:
To determine if a line is parallel, perpendicular, or neither, we primarily analyze the slopes of the lines in question. Parallel lines have the same slope, while perpendicular lines have slopes that are negative reciprocals of each other (the product of their slopes is -1).
For example, consider the equations from the question:
a. y = -3x is a straight line with a negative slope.
b. y = 0.2 + 0.74x has a positive slope.
c. y = -9.4 is a horizontal line, meaning its slope is 0.
From these examples, equations a. and b. are linear equations, and they are not parallel because their slopes are different. Equations a. and c. are neither parallel nor perpendicular as a horizontal line cannot have a negative reciprocal slope. To compare line equations, one must also look at the y-intercept, which does not affect whether lines are parallel or perpendicular but does determine if they are the same line (if they have the same slope and y-intercept).
Regarding practice test questions, every equation listed (A. y = -3x, B. y = 0.2 + 0.74x, and C. y = -9.4 - 2x) is a linear equation since they are all in the form y = mx + b, where m represents the slope and b the y-intercept.
Interpreting the slope and intercept is crucial for understanding the behavior of the line. If a line has a positive slope, such as line A in the last example, it is an increasing line. Conversely, a negative slope indicates a decreasing line. If a line is steeper, it means the absolute value of its slope is larger.