Question

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Select the following lines that would be perpendicular to y = 3x + 1. (Select ALL correct)


Question 3 options:


The line passing through points (3,8) and (6,9).



The line passing through points (1,4) and (4,3).



The line passing through points (1,-4) and (4,-5).



The line passing through points (4,3) and (5,6).

Answer 1

the answers to the questions

Answer 2

lines 3 and 4 are perpendicular to the given line.

Explanation:

The equation of line is y = 3x +1

Slope of this line = 3

Now, we know that the slopes of perpendicular lines are negative reciprocal of each other.

Hence, find the slopes of each lines and see which one is negative reciprocal of the slope of the given line.

The slope of the perpendicular line should be -1/3

Slope of a line is given by

`m=(y_2-y_1)/(x_2-x_1)`

Slope of line passing through points (3,8) and (6,9).

`m_1=(9-8)/(6-3)\\\\=(1)/(3)`

This is not perpendicular.

Slope of line passing through points (1,4) and (4,3).

`m_2=(3-4)/(4-1)\\\\=(-1)/(3)`

This is perpendicular.

Slope of line passing through points (1,-4) and (4,-5).

`m_3=(-5+4)/(4-1)\\\\=(-1)/(3)`

This is perpendicular.

Slope of line passing through points (4,3) and (5,6).

`m_4=(6-3)/(5-4)\\\\m_4=(3)/(1)\\\\m_4=3`

This is not perpendicular.

Therefore, lines 3 and 4 are perpendicular to the given line.