Question

lines rs, tv, and sw are shown.
which statements are true about these lines? choose three correct answers.

• line rs has a slope of 6.
• lines rs and tv are parallel.
• line sw is perpendicular to line rs, but not to line tv.
• line sw has an undefined slope.
• line tv has a slope of 0.

Explanation:

Identify the equations of the lines

We analyze the positions of the lines on the coordinate plane.

• Line \(RS\) is horizontal and passes through \(y = 6\).
• Line \(TV\) is horizontal and passes through \(y = -4\).
• Line \(SW\) is vertical and passes through \(x = 2\).

Determine the slopes of the lines

We calculate the slope \(m = \frac{\Delta y}{\Delta x}\) for each line.

• For horizontal lines \(RS\) and \(TV\), the change in \(y\) is \(0\), so their slopes are \(0\).
• For the vertical line \(SW\), the change in \(x\) is \(0\), which means division by zero, so its slope is undefined.

Analyze the relationships between the lines

We evaluate the parallel and perpendicular relationships.

• Since lines \(RS\) and \(TV\) both have a slope of \(0\), they are parallel to each other.
• Since line \(SW\) is vertical and lines \(RS\) and \(TV\) are horizontal, \(SW\) is perpendicular to both \(RS\) and \(TV\).

Evaluate the given statements

We test each of the five options:

1. "Line \(RS\) has a slope of 6." (False, its slope is 0).
2. "Lines \(RS\) and \(TV\) are parallel." (True, both are horizontal).
3. "Line \(SW\) is perpendicular to line \(RS\), but not to line \(TV\)." (False, it is perpendicular to both).
4. "Line \(SW\) has an undefined slope." (True, it is vertical).
5. "Line \(TV\) has a slope of 0." (True, it is horizontal).

Answer:

• Line RS has a slope of 6.
• Lines RS and TV are parallel. (Correct answer)
• Line SW is perpendicular to line RS, but not to line TV.
• Line SW has an undefined slope. (Correct answer)
• Line TV has a slope of 0. (Correct answer)