How do you graph \[4x - 3y = 6\] by plotting points?

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 solution:
Given, \[4x - 3y = 6\].
To find the x-intercept. That is the value of ‘x’ at\[y = 0\]. Substituting this in the given equation. We have,
\[\Rightarrow 4x - 3(0) = 6\]
\[\Rightarrow 4x = 6\]
Divide the whole equating by 4.
\[\Rightarrow x = \dfrac{6}{4}\]
\[\Rightarrow x = \dfrac{3}{2}\].
\[\Rightarrow x = 1.5\]
Thus we have a coordinate of the equation which lies on the line of x-axis. The coordinate is \[(1.5,0)\].
To find the y-intercept. That is the value of ‘y’ at \[x = 0\]. Substituting this in the given equation we have,
\[\Rightarrow 4(0) - 3y = 6\]
\[\Rightarrow - 3y = 6\].
\[\Rightarrow y = - \dfrac{6}{3}\]
\[\Rightarrow y = - 2\]
Thus we have a coordinate of the equation which lies on the line of y-axis. The coordinate is \[(0, - 2)\].
Thus we have the coordinates \[(1.5,0)\] and \[(0, - 2)\].
Let’s plot a graph for this coordinates,



All we did is expand the line touching the coordinates \[(1.5,0)\] and \[(0, - 2)\].
Without doing the calculation we found out two more coordinates. (See in the graph). The coordinates are \[( - 3, - 6)\] and \[(3,2)\].

Note: A graph shows the relation between two variable quantities, it contains two axes perpendicular to each other namely the x-axis and the y-axis. Each variable is measured along one of the axes. In the question, we are given one linear equation containing two variables namely x and y, x is measured along the x-axis and y is measured along the y-axis while tracing the given equations.