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

Answer:

$2x-3y+21=0$

Step-by-step explanation:

We are given that an equation

$y=-\frac{3}{2}x+4$

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

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

By comparing with

$y=mx+b$

Where m=Slope of line

Slope of given line=$=m_1=\frac{-3}{2}$

Slope of the line=$-\frac{1}{m_1}=-\frac{1}{\frac{-3}{2}}=\frac{2}{3}$

Slope of the line=$\frac{2}{3}$

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

$y-9=\frac{2}{3}(x-3)$

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

$3y-27=2x-6$

$3y=2x-6+27$

$2x-3y+21=0$