Question

1. determine which lines are parallel and which lines are perpendicular.

(-3,0) (0,2) (-2,-2) (2,3) (0, - 1) (4,2) (3,-1)
1 i dont understand yet. 2 i can do it with help. 3 i can do it on my own. 4 i can teach someone.
3.5 equations of parallel and perpendicular lines 151

Explanation:

Step1: Find the slope of line a

Use the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$ with points $(-3,0)$ and $(0,2)$. So $m_a=\frac{2 - 0}{0-(-3)}=\frac{2}{3}$.

Step2: Find the slope of line b

Use the slope formula with points $(0, - 1)$ and $(2,3)$. So $m_b=\frac{3-(-1)}{2 - 0}=\frac{4}{2}=2$.

Step3: Find the slope of line c

Use the slope formula with points $(3,-1)$ and $(4,2)$. So $m_c=\frac{2-(-1)}{4 - 3}=\frac{3}{1}=3$.

Step4: Find the slope of line d

Use the slope formula with points $(-2,-2)$ and $(0,-1)$. So $m_d=\frac{-1-(-2)}{0-(-2)}=\frac{1}{2}$.

Step5: Determine parallel and perpendicular lines

Parallel lines have equal slopes and perpendicular lines have slopes that are negative - reciprocals. Since none of the slopes are equal, there are no parallel lines. Also, since no two slopes are negative - reciprocals of each other (e.g., if $m_1$ and $m_2$ are slopes of perpendicular lines, $m_1\times m_2=-1$), there are no perpendicular lines.

Answer:

There are no parallel lines and no perpendicular lines.