Question

classify the lines as parallel, perpendicular, or neither.

Explanation:

Step1: Recall slope - relationship for line types

Parallel lines have equal slopes, perpendicular lines have slopes that are negative reciprocals.

Step2: Calculate slopes using two - point formula

Let's assume two points on the first line $(x_1,y_1)$ and $(x_2,y_2)$ and for the second line $(x_3,y_3)$ and $(x_4,y_4)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. From the graph, for the steeper line, if we take two points like $(- 10,0)$ and $(-6,6)$, the slope $m_1=\frac{6 - 0}{-6+10}=\frac{6}{4}=\frac{3}{2}$. For the flatter line, if we take two points like $(-6,6)$ and $(10, - 2)$, the slope $m_2=\frac{-2 - 6}{10 + 6}=\frac{-8}{16}=-\frac{1}{2}$.

Step3: Check the relationship between slopes

The product of the slopes $m_1\times m_2=\frac{3}{2}\times(-\frac{1}{2})=-\frac{3}{4}
eq - 1$ (not perpendicular), and $m_1
eq m_2$ (not parallel).

Answer:

Neither