Question

How do you graph $y + 4 = \dfrac{1}{3}\left( {x + 6} \right)$?

Answer 1

Hint:
In this question we asked to find the graph of the given function by plotting the points, for this we will give some values for $x$ like 0, 1, 2, 3,…… simultaneously we will get the respective values for $y$, so after getting the values for $x$ and $y$ write the coordinates of the given equation in the form $\left( {x,y} \right)$, then plotting the coordinates on the graph we will get the required graph.

Complete step by step solution:
Given a function is $y + 4 = \dfrac{1}{3}\left( {x + 6} \right)$, this is in the form of a linear equation with two variables.
Now take some values for $x$, as $x = - 6$
$ \Rightarrow y + 4 = \dfrac{1}{3}\left( {x + 6} \right)$,
Now substitute $x = - 6$in the above equation we get
$ \Rightarrow y + 4 = \dfrac{1}{3}\left( { - 6 + 6} \right)$,
Now simplifying we get,
$ \Rightarrow y + 4 = \dfrac{1}{3}\left( 0 \right)$,
Now again simplifying we get,
$ \Rightarrow y + 4 = 0$,
Now further simplifying we get,
$ \Rightarrow y = - 4$,
So the point is \[\left( { - 6, - 4} \right)\],
Now take $x = - 3$in the equation we get
$ \Rightarrow y + 4 = \dfrac{1}{3}\left( {x + 6} \right)$,
Now substitute $x = - 3$in the above equation we get,
$ \Rightarrow y + 4 = \dfrac{1}{3}\left( { - 3 + 6} \right)$,
Now simplifying we get,
$ \Rightarrow y + 4 = \dfrac{1}{3}\left( 3 \right)$,
Now again simplifying we get,
$ \Rightarrow y + 4 = 1$,
Now further simplifying we get,
$ \Rightarrow y = - 3$,
So the point is $\left( { - 3, - 3} \right)$,
Now substitute $x = 0$in the above equation we get,
$ \Rightarrow y + 4 = \dfrac{1}{3}\left( {0 + 6} \right)$,
Now simplifying we get,
$ \Rightarrow y + 4 = \dfrac{1}{3}\left( 6 \right)$,
Now again simplifying we get,
$ \Rightarrow y + 4 = 2$,
Now further simplifying we get,
$ \Rightarrow y = - 2$,
So the point is \[\left( {0, - 2} \right)\],
Now substitute $x = 3$in the above equation we get,
$ \Rightarrow y + 4 = \dfrac{1}{3}\left( {3 + 6} \right)$,
Now simplifying we get,
$ \Rightarrow y + 4 = \dfrac{1}{3}\left( 9 \right)$,
Now again simplifying we get,
$ \Rightarrow y + 4 = 3$,
Now further simplifying we get,
$ \Rightarrow y = - 1$,
So the point is \[\left( {3, - 1} \right)\],
$ \Rightarrow y + 4 = \dfrac{1}{3}\left( {x + 6} \right)$,
Now substitute $x = 6$in the above equation we get
$ \Rightarrow $$ \Rightarrow y + 4 = \dfrac{1}{3}\left( {6 + 6} \right)$,
Now simplifying we get,
$ \Rightarrow y + 4 = \dfrac{1}{3}\left( {12} \right)$,
Now again simplifying we get,
$ \Rightarrow y + 4 = 4$,
Now further simplifying we get,
$ \Rightarrow y = 0$,
So the point is \[\left( {6,0} \right)\],
Now tabulating the values we get,

$x$	$y$
-6	-4
-3	-3
0	-2
3	-1
6	0

Now tabulate the values on the graph we get,

$\therefore $The graph of the given function $y + 4 = \dfrac{1}{3}\left( {x + 6} \right)$ will be equal to,

Note:
We can represent every linear equation in two variables in a graph as a straight line in a coordinate plane. Points on the lines are known as the solution of the equation. So, the equation with one degree is known as linear equation. The expression of linear equations in a graph is known as graphing of linear equations in two variables.