which of the following pairs of lines are perpendicular? select all that apply A y=2/3x+4 and y=2/3x-8 B y=2/3x-8 and y=-3/2x-8 C y=x+3 and y=-x=3 D y=3x+n and y=3x-2 E y=3 and x=4 F y=4/5x-8 and y=-5/4x=3

Accepted Solution

Answer:Hence, B, C and F are pairs of perpendicular line.Step-by-step explanation:We have to find the pairs of line that are perpendicular to each other.Two lines are said to be perpendicular if the product of their slope is -1 that is:[tex]m_1\times m_2 = -1[/tex]The slope of each line can be calculated with the help of slope intercept form:[tex]y = mx + c[/tex]1) [tex]y=\frac{2}{3}x+4, y=\frac{2}{3}x-8\\\\m_1 = \frac{2}{3}\\\\m_2 = \frac{2}{3}\\\\m_1\times m_2 \neq -1[/tex]2)[tex]y=\frac{2}{3}x-8, y=\frac{-3}{2}x-8\\\\m_1 = \frac{2}{3}\\\\m_2 = \frac{-3}{2}\\\\m_1\times m_2 = -1[/tex]3)[tex]y=x+3, y=-x-3\\\\m_1 = 1\\\\m_2 = -1\\\\m_1\times m_2 = -1[/tex]4)[tex]y=3x+n, y=3x-2\\\\m_1 =3\\\\m_2 =3\\\\m_1\times m_2 \neq -1[/tex]5)[tex]y=3, x=4\\\\m_1 =0\\\\m_1\times m_2 \neq -1[/tex]6)[tex]y=\frac{4}{5}x-8, y=\frac{-5}{4}x-3\\\\m_1 = \frac{4}{5}\\\\m_2 = \frac{-5}{4}\\\\m_1\times m_2 = -1[/tex]Hence, B, C and F are pairs of perpendicular line.