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 - value constant). The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For horizontal line, $y_2 - y_1 = 0$, so slope $m = 0$, not 6. So "Line RS has a slope of 6" is false.

Step2: Analyze Line SW

Line SW is vertical (x - value constant). For vertical line, $x_2 - x_1 = 0$, so slope is undefined (division by zero). So "Line SW has an undefined slope" is true.

Step3: Analyze Line TV

Line TV is horizontal (y - value constant). So slope $m=\frac{y_2 - y_1}{x_2 - x_1}=0$ (since $y_2 - y_1 = 0$). So "Line TV has a slope of 0" is true.

Step4: Analyze Parallelism of RS and TV

Both RS and TV are horizontal lines (slope 0). Horizontal lines with same slope are parallel. So "Lines RS and TV are parallel" is true.

Step5: Analyze Perpendicularity of SW with RS and TV

Line SW is vertical (undefined slope), RS and TV are horizontal (slope 0). Vertical and horizontal lines are perpendicular. So SW is perpendicular to both RS and TV. So "Line SW is perpendicular to line RS, but not to line TV" is false.

Answer:

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