Question

How do you solve $y = - x - 4$ , $y = \dfrac{3}{5}x + 4$ by graphing?

Answer 1

Hint: In this question, a linear equation of two variables is given. Here we will use the graphing method to solve these two linear equations. We will plot both equations of lines on the graph. For that, we should know the condition of types of the solution of the system of linear equations. A system of linear equations has finite, infinite, or no solutions. To solve the equations using the graphing method, we should follow the below steps:
Place the linear equations in the slope-intercept form.
Graph the lines and use the graph to find the common point.

Complete step-by-step answer:
Here, we want to solve the equations using the graphing method.
$ \Rightarrow y = - x - 4$ ...(1)
$ \Rightarrow y = \dfrac{3}{5}x + 4$ ...(2)
The first step is to place the linear equations in the slope-intercept form.
As we already know, the equation of the line in the slope-intercept form is $y = mx + b$. Where m is the value of slope and b is the y-intercept. Here, m and b are constants, and x and y are variables. Since x and y are variables that describe the position of specific points on the graph, m and b describe features of the function.
In this question, both lines are already in the slope-intercept form.
Let us compare equation (1) with the slope-intercept form is $y = mx + b$.
Here, the value of slope m is -1, and the value of y-intercept b is -4.
To plot these lines we have to find the points on both lines.
Now, let us find the points on the line $y = - x - 4$ by assuming the values of x.
Take the value of x is equal to 0.
$ \Rightarrow y = - x - 4$
Put the value of x.
$ \Rightarrow y = - 0 - 4$
That is equal to,
$ \Rightarrow y = - 4$
Now, take the value of x is equal to 1.
$ \Rightarrow y = - x - 4$
Put the value of x.
$ \Rightarrow y = - 1 - 4$
That is equal to,
$ \Rightarrow y = - 5$
Now, take the value of x is equal to 2.
$ \Rightarrow y = - x - 4$
Put the value of x.
$ \Rightarrow y = - 2 - 4$
That is equal to,
$ \Rightarrow y = - 6$
Hence the points for equation (1) are:

X	0	1	2
y	-4	-5	-6

Now, let us find the points on the line $y = \dfrac{3}{5}x + 4$ by assuming the values of x.
Take the value of x is equal to 0.
$ \Rightarrow y = \dfrac{3}{5}x + 4$
Put the value of x.
$ \Rightarrow y = \dfrac{3}{5}\left( 0 \right) + 4$
That is equal to,
$ \Rightarrow y = 4$
Now, take the value of x is equal to 5.
$ \Rightarrow y = \dfrac{3}{5}x + 4$
Put the value of x.
$ \Rightarrow y = \dfrac{3}{5}\left( 5 \right) + 4$
$ \Rightarrow y = 3 + 4$
That is equal to,
$ \Rightarrow y = 7$
Now, take the value of x is equal to -5.
$ \Rightarrow y = \dfrac{3}{5}x + 4$
Put the value of x.
$ \Rightarrow y = \dfrac{3}{5}\left( { - 5} \right) + 4$
$ \Rightarrow y = - 3 + 4$
That is equal to,
$ \Rightarrow y = 1$
Hence the points for equation 21) are:

X	0	5	-5
Y	4	7	1

Let us plot the graph.

Note:
There are other methods to solve the system of the linear equation are as below.
Substitution method.
Elimination method.
We can get the same answer using any method.