Question

find out the equation of a straight line which passes through the points( 2,6) (4,2). show the line in graph also​

Answer 1

$\Large{\underline{\underline{\mathfrak{\bf{Question}}}}}$

find out the equation of a straight line which passes through the points( 2,6) (4,2). show the line in graph also .

$\Large{\underline{\underline{\mathfrak{\bf{Solution}}}}}$

$\Large{\underline{\mathfrak{\bf{\pink{Given}}}}}$

• First points A(2,6)
• Second point B(4,2)

$\Large{\underline{\mathfrak{\bf{\pink{Find}}}}}$

• Equation of straight line

$\Large{\underline{\underline{\mathfrak{\bf{Explanation}}}}}$

We know,

Equation of straight Line,

$\small\boxed{\sf{\blue{\:(y-y')\:=\:\dfrac{(y"-y')}{(x"-x')}(x-x')}}}$

Where,

• (x',y') = (2,6)
• (x",y") = (4,2)

keep value ,

$\mapsto\sf{\:(y-6)\:=\:\dfrac{(6-2)}{(4-2)}(x-2)} \\ \\ \mapsto\sf{\:(y-6)\:=\:\dfrac{4}{2}(x-2)} \\ \\ \mapsto\sf{\:(y-6)\:=\:-2(x-2)} \\ \\ \mapsto\sf{\:2x+y\:=\:6+4} \\ \\ \mapsto\sf{\:(2x+y)\:=\:10}$

$\large{\underline{\mathfrak{\bf{\pink{\:Required\:straight\:line}}}}}$

$\boxed{\sf{\blue{\:(2x+y)\:=\:10}}}$

$\large{\underline{\mathfrak{\bf{\pink{\:\:Formula\:of\:General\:straight\:line}}}}}$

$\boxed{\sf{\pink{\:y\:=\:mx+c}}}$

We can write required equation in general equation,

$\mapsto\sf{\blue{\:y\:=\:-2x+10}}$

So, compare of required equation same as general equation,

$\mapsto\sf{\:slope(m)\:=\:-2} \\ \\ \mapsto\sf{\:y\:intercept\:(c)\:=\:10}$