Question

Find the equation of the line that is perpendicular to y = – 1 3 x + 2 and passes though the point (–5, 2).
A) y = 3x + 13
B) y = 3x + 17
C) y = –3x + 13
D) y = –3x + 17

Answer 1

Answer:

The required equation is y = 3x + 17. Correct: B)

Explanation:

Equation of a line

A line can be represented by an equation of the form

y=mx+b

Where x is the independent variable, m is the slope of the line, m is the y-intercept and y is the dependent variable.

We are given the equation of a line as (corrected)

y=-1/3x+2

Note the slope of this line is m1=-1/3

We are asked to find the equation of another line that is perpendicular to the one above. Two lines are perpendicular if their slopes comply with the following condition:

$m_1*m_2=-1$

Since we have m1, find m2:

$\displaystyle m_2=-\frac{1}{m_1}$

$\displaystyle m_2=-\frac{1}{-\frac{1}{3}}=3$

This means the slope of the required line is 3. We only have to test the options to find which one of us contains the point (-5,2):

A) The slope of this line is 3, so we test the point (-5,2)

2=3(-5)+13=-15+13=-2

Since 2 is different from -2, this option is not correct

B) The slope of this line is 3, so we test the point (-5,2)

2=3(-5)+17=-15+17=2

Since equality stands, this is the correct option

C) The slope of this line is -3, it cannot be the required line. This option is not correct

D) The slope of this line is -3, it cannot be the required line. This option is not correct