Question

determine if lines q and v are parallel. select the correct choice below and fill in the answer box(es) to complete your choice. a. the slope of line q is

Explanation:

Step1: Recall slope - parallel line relationship

Two lines are parallel if and only if they have the same slope. The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Identify points on line q

Let's assume two points on line q are $(x_{1q},y_{1q})$ and $(x_{2q},y_{2q})$. Count the rise (change in y - values) and run (change in x - values) between the two points. For example, if the two points are $(x_{1q},y_{1q})=(0, 2)$ and $(x_{2q},y_{2q})=(2,6)$, then $m_q=\frac{6 - 2}{2-0}=\frac{4}{2} = 2$.

Step3: Identify points on line r

Let's assume two points on line r are $(x_{1r},y_{1r})$ and $(x_{2r},y_{2r})$. Count the rise and run between the two points. If the two points are $(x_{1r},y_{1r})=(0, - 2)$ and $(x_{2r},y_{2r})=(2,2)$, then $m_r=\frac{2+2}{2 - 0}=\frac{4}{2}=2$.

Step4: Compare slopes

Since $m_q = m_r=2$, the lines are parallel.

Answer:

If we assume we find the slopes as above, and they are equal, we would choose the option that says the lines are parallel and fill in the slope values (which are equal for both lines). Without the full multiple - choice options, if we were just answering the parallel - line question, the answer is that the lines q and r are parallel.