Question

How do you graph \[3x - 4y - 8 = 0\] by plotting points?

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 solution:
Given, \[3x - 4y - 8 = 0\].
This can be rewrite as
\[3x - 4y = 8\]
To find the x-intercept. That is the value of ‘x’ at \[y = 0\]. Substituting this in the given equation. We have,
\[3x - 4(0) = 8\]
\[3x = 8\]
Dividing by 3 on both sides,
\[x = \dfrac{8}{3}\]
\[x = 2.666\].
Rounding off we have,
\[x = 2.67\]
Thus we have a coordinate of the equation which lies on the line of x-axis. The coordinate is \[(2.67,0)\].
To find the y-intercept. That is the value of ‘y’ at \[x = 0\]. Substituting this in the given equation we have,
\[3(0) - 4y = 8\]
\[ - 4y = 8\].
Dividing by -4 on both sides
\[y = - \dfrac{8}{4}\]
\[y = - 2\]
Thus we have a coordinate of the equation which lies on the line of the y-axis. The coordinate is \[(0, - 2)\].
Thus we have the coordinate points \[(2.67,0)\] and \[(0, - 2)\].
Let’s plot a graph for this coordinates,

We take scale x-axis= 1 unit = 0.5 units
y-axis= 1 unit = 0.5 units

All we did was expand the line touching the coordinate points \[(2.67,0)\] and \[(0, - 2)\] by a straight line.
Without calculation we found out the few more coordinate points using the graph. The coordinates are \[(4,1),(2, - 0.5)\] and \[( - 2, - 3.5)\].

Note: The intercept method is an easy method to draw the graph. It will give a more accurate line in the graph. 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.