Final answer:
Parallel lines have the same slope. The given line y=3x-2 has a slope of 3, so the parallel lines are A) y=3x+1 and B) y=3x-5, each also having a slope of 3. The correct answer is option B .
Step-by-step explanation:
The student's question is related to determining which of the given equations represents a line that is parallel to the line described by the equation y=3x-2.
In the context of linear equations of the form y=mx+b, where m is the slope and b is the y-intercept, two lines are parallel if and only if they have the same slope. This is because the slope defines the steepness and direction of a line, and for two lines to run alongside each other without intersecting, they must have identical slopes.
Since the given line y=3x-2 has a slope of 3, we are looking for an equation where the coefficient of x, which represents the slope, is also 3. Comparing the options provided:
- A) y=3x+1 - This equation has a slope of 3, making it parallel to y=3x-2.
- B) y=3x-5 - This also has a slope of 3 and is therefore parallel to y=3x-2.
- C) y=-3x+2 - The slope here is -3 which is the negative reciprocal of 3, meaning this line is perpendicular, not parallel.
- D) y=-2x+4 - The slope here is -2, which is neither the same as 3 nor the negative reciprocal, so it is neither parallel nor perpendicular.
Given this analysis, both A) y=3x+1 and B) y=3x-5 are parallel to the line y=3x-2.