Question

How do you graph $x + 2y = 6$ by plotting points?

Answer 1

Hint: In this question, we are given an equation of a line and we have been asked to draw the line on a graph. In order to draw it on a graph, find the point that lies on the graph. You can find the points by keeping different values of $x$ and then using them, find the values of $y$. Find at least three points and plot them on a graph paper. Join the points using a scale and you will have your required line.

Complete step-by-step solution:
In this question, we are given an equation of a line $x + 2y = 6$ and we have been asked to plot this on the graph.
Let us find the points.
1) Let $x = 0$. Put this in the equation.
$ \Rightarrow 0 + 2y = 6$
Shifting to find the value of $y$,
$ \Rightarrow y = \dfrac{6}{2} = 3$
It gives us the point $\left( {0,3} \right)$. We will name it A.
Therefore, our first point is A$\left( {0,3} \right)$.
2) Let $y = 0$. Put this in the equation.
$ \Rightarrow x + 0 = 6$
$ \Rightarrow x = 6$
It gives us the point $\left( {6,0} \right)$. We will name it as B.
Therefore, our first point is B$\left( {6,0} \right)$.
3) Let $x = 2$. Put this in the equation.
$ \Rightarrow 2 + 2y = 6$
Shifting to find the value of $y$,
$ \Rightarrow 2y = 6 - 2 = 4$
$ \Rightarrow y = \dfrac{4}{2} = 2$
It gives us the point $\left( {2,2} \right)$. We will name it as C.
Therefore, our first point is C$\left( {2,2} \right)$.
Let us plot the three points on the graph.

Next step is to connect these points. Keep in mind to use a scale.

Hence, this is our final answer.

Note: In such questions, always find at least three points as there is step marking in exams and they need you to find three points.
An easy trick in such questions is to find points on the two axes by keeping $x = 0$ and then, $y = 0$. Only by plotting these two points, you will get a perfect line.