Question

Draw the graph of the equation x− 2y = 6 .Shade the triangle formed by the line and the two axes. Also find the area of the triangle
Pls do it a graph pllsssss

pls answer its veryy urgent

Answer 1

EXPLANATION.

Graph of the equation.

⇒ x - 2y = 6.

As we know that,

Put the value of x = 0 in the equation, we get.

⇒ (0) - 2y = 6.

⇒ - 2y = 6.

⇒ y = - 3.

Their Co-ordinates = (0,-3).

Put the value of y = 0 in the equation, we get.

⇒ x - 2(0) = 6.

⇒ x = 6.

Their Co-ordinates = (6,0).

As we know that,

Area of triangle = 1/2 x Base x Height.

⇒ Height = - 3.

⇒ Base = 6 - 0 = 6.

Area of triangle = 1/2 x 6 x (-3).

Area of triangle = - 9 sq. units.

Area cannot be negative, So - 9 = |-9| = 9 sq. units.

Answer 2

⠀⠀⠀⠀⠀⠀Graph of Equation : ❝ x - 2y = 6 ❞

▪︎We know that , to draw a graph of Equation in two variable in a pair of number ( x , y ) we need to have atleast two solutions of Given Equation ❝ x - 2y = 6 ❞ :

⠀⠀⠀⠀⠀⠀~ Finding Solution of Given Equation ❝ x - 2y = 6 ❞ :

⠀⠀⠀• Putting ❝ x = 0 ❞ , We get ,

$\qquad \dashrightarrow \sf x - 2y = 6 \:\: \\\\ \qquad \dashrightarrow \sf (0) - 2y = 6 \:\: \\\\\qquad \dashrightarrow \sf - 2y = 6 \:\: \\\\ \qquad \dashrightarrow \sf y = \dfrac{6}{-2} \:\: \\\\ \qquad \dashrightarrow \underline {\boxed {\pmb{\frak{ y\: =\: -\: 3 \:}}}}\:\:\bigstar \:$

⠀⠀⠀⠀⠀⠀ So , ❝ ( 0 , - 3 ) ❞ is a solution of a Equation.

⠀⠀⠀• Putting ❝ y = 0 ❞ , We get ,

$\qquad \dashrightarrow \sf x - 2y = 6 \:\: \\\\ \qquad \dashrightarrow \sf x - 2(0) = 6 \:\: \\\\\qquad \dashrightarrow \sf x - 0 = 6 \:\: \\\\ \qquad \dashrightarrow \sf x = 6 \:\: \\\\ \qquad \dashrightarrow \underline {\boxed {\pmb{\frak{ x\: =\: 6\: \:}}}}\:\:\bigstar \:$

⠀⠀⠀⠀⠀⠀ So , ❝ ( 6 , 0 ) ❞ is a solution of a Equation.

⠀⠀➟ By Plotting these co – ordinates [ ( 0 , - 3 ) & ( 6 , 0 ) ] we had made a graph of Equation ❝ x - 2y = 6 ❞ .

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀¤ Finding Area of Triangle formed by graph :

As , We know that,

$\qquad \star \:\:\underline {\boxed {\pmb{\sf { \:\:Area\:_{\:(\:Triangle \:)} \:= \:\dfrac{1}{2} \:\times \:Base \:\times \: Height \:sq.units \:}}}}\:\:$

⠀⠀⠀⠀⠀ By Observing we get ,

• Base of Triangle is : 6 units &
• Height of Triangle is : - 3 units .

$\qquad \dashrightarrow \sf Area\:_{\:(\:Triangle \:)} \:= \:\dfrac{1}{2} \:\times \:Base \:\times \: Height \:\\\\\\ \qquad \dashrightarrow \sf Area\:_{\:(\:Triangle \:)} \:= \:\dfrac{1}{2} \:\times \:6 \:\times \: ( - 3 ) \:\\\\\\ \qquad \dashrightarrow \sf Area\:_{\:(\:Triangle \:)} \:= \: 3 \:\times \: (-3) \:\\\\\\ \qquad \dashrightarrow \sf Area\:_{\:(\:Triangle \:)} \:= \:-\:9 \:$

• Area of Triangle cannot be in " - ve " sign .

$\qquad \dashrightarrow \sf Area\:_{\:(\:Triangle \:)} \:= \:-9 \:\\\\ \qquad \dashrightarrow \sf Area\:_{\:(\:Triangle \:)} \:= \:|\:-9\:| \:\\\\ \qquad \dashrightarrow \sf Area\:_{\:(\:Triangle \:)} \:= \:9 \:\\\\\qquad \dashrightarrow \underline {\boxed {\pmb{\frak{ \:Area\:_{\:(\:Triangle \:)} \:= \:9 \:sq.units \:}}}}\:\:\bigstar \:$

⠀∴ Hence , The Area of Triangle is 9 sq.units .