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Which one of the following graphs represents the linear equation $2 x + 3 y = 12$ ? And at what points, the graph of the equation cuts the $x$ -axis and the $y$ -axis?

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(6, 0), (0, 4)

Chart, line chart

Description automatically generated

(6, 0), (0, - 4)

(4, 0), (0, - 4)

(4, 0), (0, 6)

answer is A.

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Detailed Solution

Given equation,

2 x + 3 y = 12 .

To draw the graph of the equation, we used the plotted point method,

x	y
0	4
6	0
1	$\frac{10}{3}$

Using the above table, the graph can be obtained as:
Question Image

From the above graph it can be observed that the points where the graph of the equation cuts the

x - axis

and

y - axis

are

(6, 0), (0, 4)

respectively.
Or
Putting the value of x = 0(y-axis), in the equation

2 x + 3 y = 12

to get the value of y

3 y = 12

y = 4

. Putting the value of y = 0(x-axis), in the equation

2 x + 3 y = 12

to get the value of x

2 x = 12

x = 6

. Therefore, the points where line cuts the

x - axis

and

y - axis

are

(6, 0), (0, 4)

respectively.
Therefore, option 1) is correct.

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