Question

How do you graph the equation \[2x + y = - 6\]?

Answer 1

Hint: To solve this we need to give the values of ‘x’ and we can find the values of ‘y’. Otherwise we can find the coordinate of the given equation lying on the line of x- axis, we can find this by substituting the value of ‘y’ is equal to zero (x-intercept). Similarly we can find the coordinate of the equation lying on the line of y- axis, we can find this by substituting the value of ‘x’ equal to zero (y-intercept).

Complete step by step answer:
Given, \[2x + y = - 6\].
To find the x-intercept. That is the value of ‘x’ at\[y = 0\]. Substituting this in the given equation. We have,
\[2x + (0) = - 6\]
\[2x = - 6\]
Dividing by 2 on both sides,
\[x = \dfrac{{ - 6}}{2}\]
\[ \Rightarrow x = - 3\].
Thus we have a coordinate of the equation which lies on the line of x-axis. The coordinate is \[( - 3,0)\].
To find the y-intercept. That is the value of ‘y’ at \[x = 0\]. Substituting this in the given equation we have,
\[2(0) + y = - 6\]
\[ \Rightarrow y = - 6\].
Thus we have a coordinate of the equation which lies on the line of the y-axis. The coordinate is \[(0, - 6)\].
Thus we have the coordinates \[( - 3,0)\] and \[(0, - 6)\].
Let’s plot a graph for this coordinates,
We take scale x-axis= 1 unit = 1 units
y-axis= 1 unit = 1 units

All we did is expand the line touching the coordinates \[( - 3,0)\] and \[(0, - 6)\] by a straight line.
Using the graph we have found out three more coordinates, those are \[( - 2, - 2)\] and \[( - 1, - 4)\].


Note: Using the intercept method is easy and we get the graph more accurately with coordinate points. In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represented the relationship between two or more things.