Question

Draw the graph of equationx + 2y = 7. Also find the area of the region bounded by co-ordinate axis and the line.​

Answer 1

EXPLANATION.

Graph of the equation.

⇒ x + 2y = 7.

As we know that,

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

⇒ (0) + 2y = 7.

⇒ 2y = 7.

⇒ y = 3.5.

Their Co-ordinates = (0,3.5).

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

⇒ x + 2(0) = 7.

⇒ x = 7.

Their Co-ordinates = (7,0).

Area of the bounded region by Co-ordinates axis and the line.

As we know that,

Formula of Δ = 1/2 x base x height.

In base always count x-axis.

in height always count y-axis.

⇒ Area of Δ = 1/2 x 7 x 3.5.

⇒ Area of Δ = 12.25 sq. units.

Answer 2

Solution :-

At first putting x as 0

$\sf 0 + 2y=7$

$\sf 2y = 0 +7$

$\sf 2y = 7$

$\sf y = \dfrac{7}{2}$

$\sf y = 3.5$

Then putting y as 0

$\sf x +2(0) = 7$

$\sf x+0=7$

$\sf x=0+7$

$\sf x =7$

So,

Co-ordinates of x = 0,3.5

Co-ordinates of y = 0,7

$\sf Area = \dfrac{1}{2} \times base \times height$

$\sf Area = \dfrac{1}{2}\times3.5\times 7$

$\sf Area = 3.5\times3.5$

$\sf Area = 12.25 \;$