Question

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

Answer 1

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:

$m_1\times m_2 = -1$

The slope of each line can be calculated with the help of slope intercept form:

$y = mx + c$

1)

$y=\frac{2}{3}x+4, y=\frac{2}{3}x-8\\\\m_1 = \frac{2}{3}\\\\m_2 = \frac{2}{3}\\\\m_1\times m_2 \neq -1$

2)

$y=\frac{2}{3}x-8, y=\frac{-3}{2}x-8\\\\m_1 = \frac{2}{3}\\\\m_2 = \frac{-3}{2}\\\\m_1\times m_2 = -1$

3)

$y=x+3, y=-x-3\\\\m_1 = 1\\\\m_2 = -1\\\\m_1\times m_2 = -1$

4)

$y=3x+n, y=3x-2\\\\m_1 =3\\\\m_2 =3\\\\m_1\times m_2 \neq -1$

5)

$y=3, x=4\\\\m_1 =0\\\\m_1\times m_2 \neq -1$

6)

$y=\frac{4}{5}x-8, y=\frac{-5}{4}x-3\\\\m_1 = \frac{4}{5}\\\\m_2 = \frac{-5}{4}\\\\m_1\times m_2 = -1$

Hence, B, C and F are pairs of perpendicular line.

Answer 2

From the pair of lines, the ones which are perpendicular are:

B. y=2/3x-8 and y=-3/2x-8

C. y=x+3 and y=-x=3

F. y=4/5x-8 and y=-5/4x=3

The equation of a straight line is:

y = mx + b;

y, x are variables, m is the slope of the line and b is the y intercept.

Two lines are said to be perpendicular if the product of their slopes is -1. Hence the slopes are negative inverse of each other.

From the pair of lines, the ones which are perpendicular are:

B. y=2/3x-8 and y=-3/2x-8

C. y=x+3 and y=-x=3

F. y=4/5x-8 and y=-5/4x=3

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