draw the graph of the equation x/3 + y/4 = 1 also find the area of the triangle formed - Maths - Linear Equations in Two Variables

Question

draw the graph of the equation x/3 + y/4 = 1 also find the area
of the triangle formed by the two triangles formed by the line and
the coordinate axes find the area of shaded region

Ankush Jain · Accepted Answer

Given equation is $\frac{x}{3} + \frac{y}{4} = 1$

⇒ 4x + 3y = 12

Now, we have to find three solutions of the equation to plot the graph.

We can rewrite the given equation as

$x = \frac{12 - 3 y}{4}$

On putting

x = 0, we obtain y = 4

y = 0, we obtain x = 3

y = 1, we obtain x = 2.25

These solution can be represented in tabular form as follows:

x	0	3	2.25
y	4	0	1

Now by ploting the points (0, 4), (3, 0) and (2.25, 1),

we obtain the following graph.

The Area of shaded region = Area of ∆ABC

$= \frac{1}{2} \times BC×AB = \frac{1}{2} \times 3 \times 4 = 6 {Unit}^{2}$

The Area of shaded region = Area of âˆ†ABC $= \frac{1}{2} \times BC×AB = \frac{1}{2} \times 3 \times 4 = 6 {Unit}^{2}$

draw the graph of the equation x/3 + y/4 = 1. also find the area of the triangle formed by the two triangles formed by the line and the coordinate axes. find the area of shaded region.