Question

Mick is trying to determine whether the following two lines are parallel or perpendicular. y=−25x+7 y=52x−2 Which statement is true? 1. Two lines are parallel because they have the same slope, but different y-intercepts. 2. Two lines are perpendicular because their slopes are opposite reciprocals. 3. Neither - they are not parallel nor perpendicular. (1 point) Statement # is correct.

Answer 1

To determine the relationship between the two lines given by their equations, we must first identify their slopes.

The equations are:
1. \( y = -25x + 7 \)
The slope (m) of this line is \( -25 \).

2. \( y = 52x - 2 \)
The slope (m) of this line is \( 52 \).

Now, we evaluate the relationship between the slopes:

- **Parallel Lines**: Two lines are parallel if they have the same slope. In this case, the slopes are \( -25 \) and \( 52 \), which are not the same. Therefore, the lines are not parallel.

- **Perpendicular Lines**: Two lines are perpendicular if the product of their slopes is \( -1 \). We check the product of the slopes:
\[
-25 \times 52 = -1300
\]
Since \( -1300 \) is not equal to \( -1 \), the lines are not perpendicular either.

Given this analysis, the correct statement is:
3. Neither - they are not parallel nor perpendicular.

So, Statement #3 is correct.