Question

Write the equation of the line that is perpendicular to y = -2/3 x +2 and goes through the point (-1, 4). Make sure your final answer is in slope-intercept form

Answer 1

Given:

The equation of a line is

`y=-(2)/(3)x+2` ...(i)

The perpendicular line passes through the point (-1,4).

To find:

The equation of the perpendicular line.

Solution:

The slope intercept form of a line is:

`y=mx+b` ...(ii)

Where, m is the slope and b is the y-intercept.

On comparing (i) and (ii), we get

`m=-(2)/(3)`

Product of slopes of two perpendicular lines is -1.

Let the slope of perpendicular line is
`m_1`.

`m* m_1=-1`

`-(2)/(3)* m_1=-1`

`m_1=(3)/(2)`

The slope of the perpendicular line is
`m_1=(3)/(2)` and it passes through the point (-1,4). So, the equation of the line is:

`y-y_1=m_1(x-x_1)`

`y-4=(3)/(2)(x-(-1))`

`y-4=(3)/(2)(x+1)`

`y-4=(3)/(2)x+(3)/(2)`

Add 4 on both sides.

`y-4+4=(3)/(2)x+(3)/(2)+4`

`y=(3)/(2)x+(3+8)/(2)`

`y=(3)/(2)x+(11)/(2)`

Therefore, the equation of required line is
`y=(3)/(2)x+(11)/(2)`.