Question

Which of the following pairs of lines are perpendicular? Select all that apply.​

Answer 1

Answer:

• y = $\frac{2}{3}$x - 8 and y = -$\frac{3}{2}$x - 8
• y = x + 2 and y = -x + 3
• y = 3 and x = 4
• y = $\frac{4}{5}$x - 8 and y = -$\frac{5}{4}$x + 3

Step-by-step explanation:

Two lines are perpendicular to each other if the product of their slopes is -1

In the case of lines y = 3 and x = 4 , their slopes are zero and infinite respectively but this two lines are by construction perpendicular to each other.

Answer 2

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.

$m_1\times m_2=-1$

The slope intercept form is: $y=mx+c$

Where m is the slope of line.

Now consider the provided options:

Option A) $y=\frac{2}{3}x+4\ and\ y= \frac{2}{3}x-8$

Both the equation have same slope i.e 2/3.

Thus, the pair of line is not perpendicular.

Option B) $y=\frac{2}{3}x-8\ and\ y= -\frac{3}{2}x-8$

$\frac{2}{3}\times -\frac{3}{2}=-1$

Hence, the pair of line is perpendicular.

Option C) $y=x+2\ and\ y= -x+3$

$1\times \frac{1}{-1}=-1$

Hence, the pair of line is perpendicular.

Option D) $y=3x+2\ and\ y=3x-2$

Both the equation have same slope i.e 3.

Thus, the pair of line is not perpendicular.

Option E) $y=3\ and\ x=4$

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)$y=\frac{4}{5}x-8\ and\ y= -\frac{5}{4}x+3$

$\frac{4}{5}\times -\frac{5}{4}=-1$

Thus, the pair of line is perpendicular.

Hence, the correct options are: B, C, E and F