Question

which of the following is the equation of a line perpendicular to the line y= -3/2x+4 and passes through the points (3,9)

Answer 1

line y= -3/2x+4 slope = -3/2
perpendicular lines, slope is opposite and reciprocal
so slope of perpendicular line = 2/3
passes through the points (3,9)
y = mx + b
9 = 2/3(3) + b
9 = 2 + b
b = 7

equation of perpendicular line
y = 2/3x + 7
3y = 2x + 21
-2x + 3y = 21

Answer 2

`2x-3y+21=0`

Explanation:

We are given that an equation

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

We have to find an equation of line which is perpendicular to given line and passing through the point (3,9).

We know that when two lines of slope
`m_1\;and\;m_2` are perpendicular then

`m_1=-(1)/(m_2)`

By comparing with

`y=mx+b`

Where m=Slope of line

Slope of given line=
`=m_1=(-3)/(2)`

Slope of the line=
`-(1)/(m_1)=-(1)/((-3)/(2))=(2)/(3)`

Slope of the line=
`(2)/(3)`

The equation of line passing through the point (3,9) is given by

`y-y_0=m(x-x_0)`

Substitute the values

The equation of line which passing through the point (3,9) is given by

`y-9=(2)/(3)(x-3)`

`3y-27=2(x-3)`

`3y-27=2x-6`

`3y=2x-6+27`

`2x-3y+21=0`