Question

Write down the equation of the line parallel to x - 2y + 8 = 0 passing through the point (1, 2).​

Answer 1

EXPLANATION.

→ equation of line parallel to → x - 2y + 8 = 0

→ passing through the point (1,2)

→ slope of the parallel lines = -a/b

→ x - 2y + 8 = 0 → -1/ -2 = 1/2

→ equation of line.

→ ( y - y¹ ) = m ( x - x¹ )

→ ( y - 2 ) = 1/2 ( x - 1 )

→ 2 ( y - 2 ) = x - 1

→ 2y - 4 = x - 1

→ x - 2y = -3 = 0

More information.

(1) = Slope formula.

→ line joining two point ( x¹ , y¹ ) and ( x² , y ² )

→ ( y² - y¹ ) / ( x² - x¹ )

→ y² → denotes = y2

→ x² → denotes = x2

(2) = angle between two straight lines.

$\sf : \implies \: \tan( \theta) = | \dfrac{ m_{1} - m_{2} }{1 + m_{1} m_{2}} |$

(3) = Two lines.

→ ax + by + c = 0 and a'x + b'y + c = 0

are two lines.

$\sf : \implies \: parallel \: if \: \dfrac{a}{a '} = \dfrac{b}{b '} \ne \: \dfrac{c}{c '}$

→ perpendicular if → aa' + bb' = 0

→ Distance between two parallel lines.

$\sf : \implies \: = | \dfrac{ c_{1} - c_{2} }{ \sqrt{ {a}^{2} + {b}^{2} } } |$

Answer 2

$\huge\bf{\underline{\underline{\gray{GIVEN:-}}}}$

• The equation of a line is 'x - 2y + 8 = 0' .

• And the line passes through a point (1 , 2) .

$\huge\bf{\underline{\underline{\gray{TO\:FIND:-}}}}$

• The equation of the line .

$\huge\bf{\underline{\underline{\gray{SOLUTION:-}}}}$

✪ The slope of the line is,

$\bf{\implies\:Slope\:=\:-\Big(\dfrac{1}{-2}\Big)\:}$

$\bf\green{\implies\:Slope\:=\:\dfrac{1}{2}\:}$

☞︎︎︎ Let the required line be,

• $\bf\red{y\:=\:ln\:x\:+\:c}$

$\bf{\implies\:y\:=\:\dfrac{1}{2}\:x\:+\:c\:}$----(1)

☯︎ According to the question, the line passes through a point (1 , 2) .

$\rm{\implies\:2\:=\:\dfrac{1}{2}\times{1}\:+\:c\:}$

$\rm{\implies\:2\:=\:\dfrac{1}{2}\:+\:c\:}$

$\rm{\implies\:c\:=\:2\:-\:\dfrac{1}{2}\:}$

$\rm{\implies\:c\:=\:\dfrac{4\:-\:1}{2}\:}$

$\bf{\implies\:c\:=\:\dfrac{3}{2}\:}$

☞︎︎︎ Now, putting the value of 'c' in the equation 1,

$\rm{\implies\:y\:=\:\dfrac{1}{2}\:x\:+\:\dfrac{3}{2}\:}$

$\rm{\implies\:y\:=\:\dfrac{x\:+\:3}{2}\:}$

$\rm{\implies\:2y\:=\:x\:+\:3\:}$

$\bf\purple{\implies\:\:x\:-\:2y\:+\:3\:=\:0\:}$

$\huge\orange\therefore$ The required equation of the line is 'x - 2y + 3 = 0' .