Question

How do you graph the line $x+y=2?$

Answer 1

Hint: We will take some $x$ values to graph the line. And then we put those $x$ values in the given equation to find the corresponding $y$ values. So, we will get as many points as the $x$ values taken on the plane through which the given line passes.

Complete step by step solution:
Let us consider the given equation $x+y=2.$
We convert this equation into the form $y=mx+c$ which is the slope intercept form of a line where $m$ is the slope of the line. Linear equations can be converted into the slope intercept form by necessary rearrangements.
In this problem, we can transpose the variable $x$ from the left-hand side of the equation to the right-hand side of the equation. Then, the sign of the variable $x$ will change. That is, the variable $x$ will become $-x$ on the right-hand side of the equation.
We will get $y=-x+2.$
It is clear that the slope $m$ of the line is equal to $-1.$
Now let us take the following three numbers $0,1,2$ for $x$ values.
Our next task is to find the corresponding $y$ values so that we can find the points through which the required line passes.
First, let us apply $0$ for $x$ in the equation. We will get $y=0+2=2.$
So, the first point is $\left( 0,2 \right).$
Next, we apply $1$ for $x$ in the equation. We will get $y=-1+2=1.$
Therefore, the second point is $\left( 1,1 \right).$
And now we apply $2$ in the place of $x$ and that will give us $y=-2+2=0.$
The third point is $\left( 2,0 \right).$
We have obtained three points through which the line passes.
Hence the graph of the line $x+y=2$ is

Note: To graph a line, we just need two points. So, we could draw the graph only by using the points $\left( 0,2 \right)$ and $\left( 2,0 \right).$ Also, an interesting fact to remember is that every point on the line satisfies the given equation.