Answer:
The correct options are: B, C, E and F
Step-by-step explanation:
Consider the provided information.
Two lines are said to be perpendicular if the slopes are opposite reciprocals.
[tex]m_1\times m_2=-1[/tex]
The slope intercept form is: [tex]y=mx+c[/tex]
Where m is the slope of line.
Now consider the provided options:
Option A) [tex]y=\frac{2}{3}x+4\ and\ y= \frac{2}{3}x-8[/tex]
Both the equation have same slope i.e 2/3.
Thus, the pair of line is not perpendicular.
Option B) [tex]y=\frac{2}{3}x-8\ and\ y= -\frac{3}{2}x-8[/tex]
[tex]\frac{2}{3}\times -\frac{3}{2}=-1[/tex]
Hence, the pair of line is perpendicular.
Option C) [tex]y=x+2\ and\ y= -x+3[/tex]
[tex]1\times \frac{1}{-1}=-1[/tex]
Hence, the pair of line is perpendicular.
Option D) [tex]y=3x+2\ and\ y=3x-2[/tex]
Both the equation have same slope i.e 3.
Thus, the pair of line is not perpendicular.
Option E) [tex]y=3\ and\ x=4[/tex]
y=3 is a horizontal line parallel to x-axis and x=4 is a vertical line parallel to y axis. We know that x and y axis are perpendicular to each other and the provided lines follows the same property.
Thus, the pair of line is perpendicular.
Option F)[tex]y=\frac{4}{5}x-8\ and\ y= -\frac{5}{4}x+3[/tex]
[tex]\frac{4}{5}\times -\frac{5}{4}=-1[/tex]
Thus, the pair of line is perpendicular.
Hence, the correct options are: B, C, E and F
