Question

lines rs, tv, and sw are shown. which statements are true about these lines? select three options. line rs has a slope of 6. line sw has an undefined slope. line tv has a slope of 0. lines rs and tv are parallel. line sw is perpendicular to line rs, but not to line tv.

Explanation:

Step1: Analyze Line RS

Line RS is horizontal (y - coordinate constant). The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For RS, $y_1 = y_2 = 6$, so $m=\frac{6 - 6}{x_2 - x_1}=0$. So "Line RS has a slope of 6" is false.

Step2: Analyze Line SW

Line SW is vertical (x - coordinate constant). For a vertical line, $x_2=x_1$, so the slope formula gives a division by zero, meaning the slope is undefined. So "Line SW has an undefined slope" is true.

Step3: Analyze Line TV

Line TV is horizontal (y - coordinate constant, $y=-4$). Using the slope formula, $m=\frac{-4-(-4)}{x_2 - x_1}=0$. Wait, no: Wait, TV is horizontal, so slope is 0? Wait, no, wait the y - coordinates for TV are the same, so slope is 0? Wait, no, the option says "Line TV has a slope of 0" – let's check. For TV, points T and V: let's say T is (-8, -4), V is (8, -4). Then $m=\frac{-4-(-4)}{8 - (-8)}=\frac{0}{16}=0$. Wait, but wait, earlier RS has slope 0, TV has slope 0? Wait, but let's re - check the graph. RS is at y = 6 (horizontal), TV is at y=-4 (horizontal), SW is vertical at x = 2.

Step4: Analyze Parallel Lines RS and TV

Since both RS and TV are horizontal lines (slope = 0), they are parallel (parallel lines have equal slopes). So "Lines RS and TV are parallel" is true.

Step5: Analyze Perpendicularity of SW with RS and TV

A vertical line (SW, slope undefined) is perpendicular to horizontal lines (RS and TV, slope 0), because the product of a slope of 0 and an undefined slope - related (vertical and horizontal lines are perpendicular). So "Line SW is perpendicular to line RS, but not to line TV" is false, because SW is perpendicular to both.

Wait, let's re - evaluate each option:

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

So the three true options are: Line SW has an undefined slope, Line TV has a slope of 0, Lines RS and TV are parallel.

Answer:

• Line SW has an undefined slope.
• Line TV has a slope of 0.
• Lines RS and TV are parallel.