Question

the equation of the line passing through (3,5) and parallel to the line joining (-1,2)&(2,4) is​

Answer 1

Answer

2x - 3y + 9 = 0

Given:

• The line passes through (3,5)
• The line is parallel to the line joining (-1,2)&(2,4)

To Find:

• The equation of the line

If two lines are parallel then one line is as steep as the other one. i.e. their slope is same. After getting the slope for the line, we may use the slope-point formula to find the required equation

let's call the original line 'line a' and its parallel line 'line b'

For line b:

$~~\bullet~~(x_1,y_1)=(-1,2)$

$~~\bullet~~(x_2,y_2)=(2,4)$

$\boxed{Slope = \dfrac{\triangle y}{\triangle x} = \dfrac{y_2-y_1}{x_2-x_1}}$

$Slope =\dfrac{4-2}{2-(-1)}=\dfrac{2}{3}$

So, slope of line a is 2/3 too.

Slope Point Formula

$\boxed{(y-y_1)=Slope \times (x-x_1)}$

$\rm(Substituting \: 3 \: and \: 5 \: as \: x_1 \: and \: y_1 )$

$\implies (y-5)=\dfrac{2}{3}\times (x-3)$

$\implies 3 (y-5)=2(x-3)$

$\implies 3y - 15 =2x - 6$

$\implies 3y -2x-9 =0$

$\implies 2x-3y+9 =0$

2x - 3y + 9 = 0 is the required equation