Question

Draw the graph of the equation, 2x+y =6.Find the coordinate of the point where the graph cuts x-axis.

Answer 1

the line cuts x-axis at (3,0)

Answer 2

Answer:  The graph is shown in the attached figure below and the required point on the X-axis is P(3, 0).

Step-by-step explanation:  We are given to draw the graph of the following linear equation :

$2x+y=6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Also, to find the co-ordinates of the point where the graph cuts the X-axis.

From equation (i), we have

$2x+y=6\\\\\Rightarrow y=6-2x.$

So, if x = 1, then y = 6 - 2 × 1 = 6 - 2 = 4.

And, if x = 2, then y = 6 - 2 × 2 = 6 - 4 = 2.

That is, A(1, 4) and B(2, 2) are two points on the line graph of equation (i).

As shown in the attached figure below, these two points are joined to form a straight line.

This straight line is the graph of the given equation.

Now, the y co-ordinate of the point where the graph cuts the X-axis is 0.

Putting y = 0 in equation (i), we get

$2x+0=6\\\\\Rightarrow 2x=6\\\\\Rightarrow x=\dfrac{6}{2}\\\\\Rightarrow x=3.$

Thus, the required point on the X-axis is P(3, 0).