Question

How do you graph $x + y = 4$?

Answer 1

Here, we will substitute the different values of $x$ in the given equation to get the corresponding values of $y$. From this we will get the coordinate points and using these points we will draw the required graph.

Complete step-by-step answer:
The given equation is a linear equation in two variables as it is having two variables $x$ and $y$.
Now, as we know that a linear equation in two variables can have infinitely many solutions.
Thus, we will write the given equation $x + y = 4$ such that $x$ becomes an independent and $y$ becomes a dependent variable. This means that $x$ can take any value whereas the value taken by $y$ will depend on it.
Thus, the given equation can be written as:
$y = 4 - x$
Here, substituting $x = 0$, we get,
$y = 4 - 0 = 4$
Then, substituting $x = 2$, we get,
$y = 4 - 2 = 2$
And, substituting $x = 4$, we get,
$y = 4 - 4 = 0$
Therefore, we can make the following table:

X	0	2	4
Y	4	2	0

Hence, we will plot the points $\left( {0,4} \right),\left( {2,2} \right),\left( {4,0} \right)$ on the graph to show the given equation.

Therefore, this is the required answer.

Note:
An equation is called linear equation in two variables if it can be written in the form of $ax + by + c = 0$ where $a,b,c$ are real numbers and $a \ne 0$ , $b \ne 0$ as they are coefficients of $x$ and $y$ respectively. Also, the power of linear equations in two variables will be 1 as it is a ‘linear equation’. Also, a linear equation in two variables can sometimes have infinitely many solutions rather than only one in the case of ‘one variable’. The graph of a linear equation is always a straight line.