lines rs, tv, and sw are shown. which statements are true about these lines? select three options. line rs…

Explanation:

Step1: Recall slope - formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For a horizontal line, $y_2=y_1$, so $m = 0$. For a vertical line, $x_2=x_1$, and the slope is undefined.

Step2: Analyze line RS

Line RS is a horizontal line. Let's assume two points on line RS, say $R(x_1,y)$ and $S(x_2,y)$. Using the slope formula $m_{RS}=\frac{y - y}{x_2 - x_1}=0$.

Step3: Analyze line SW

Line SW is a vertical line. Let's assume two points on line SW, say $S(x,y_1)$ and $W(x,y_2)$. Using the slope formula $m_{SW}=\frac{y_2 - y_1}{x - x}$, which is undefined.

Step4: Analyze line TV

Line TV is a horizontal line. Let's assume two points on line TV, say $T(x_1,y)$ and $V(x_2,y)$. Using the slope formula $m_{TV}=\frac{y - y}{x_2 - x_1}=0$.

Step5: Check parallel and perpendicular relationships

Horizontal lines are parallel to each other. A vertical line is perpendicular to a horizontal line. Since RS and TV are horizontal, they are parallel. And SW (vertical) is perpendicular to both RS and TV (horizontal).

Answer:

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