Answer :
Final answer:
Two lines are parallel if they have the exact same slope and different y-intercepts. Option A is correct, stating that lines L₁ and L₂ are parallel because they have the same slope.
Explanation:
In determining whether lines L1 and L2 are parallel, we focus on their slopes. Two lines are parallel if and only if they have the same slope and different y-intercepts. If lines L1 and L2 both have the same slope without coinciding, then they are parallel. For instance, if the slope (m) of L1 is 2 and the slope of L2 is also 2, and they have different y-intercepts, then the lines are indeed parallel.
However, if L1 and L2 have different slopes, they are not parallel and will eventually intersect at some point, unless the different slopes indicate that the lines are perpendicular. For example, if L1 has a slope of -2 and L2 has a slope of 2, these lines are not parallel and instead they are perpendicular.
Based on the choices provided, option A is the correct one: Yes, lines L1 and L2 are parallel because they have the same slope.
Final answer:
Lines L1 and L2 are not parallel because they have different slopes; line A is an increasing line with a positive slope, while line B is a decreasing line with a negative slope.
Explanation:
To determine whether two lines, L1 and L2, are parallel, we need to compare their slopes. If the slopes are the same, and they do not lie on top of each other (they are not the same line), then the lines are parallel. However, if the slopes are different, the lines will eventually intersect at some point, meaning they are not parallel.
Based on the information provided, line A is an increasing line with a much steeper slope compared to line B which is a decreasing line. This indicates that line A has a positive slope while line B has a negative slope, meaning they are not parallel as they have different slopes.
Consequently, the correct answer to the question is:
D. No, lines L1 and L2 are not parallel because they have different slopes.
