Question

Explain how one is able to construct a graph of the given equation:
 $ - x + 2y = 1 $

Answer 1

Hint: Observe the given equation very carefully, and identify the variables given. When a linear equation is given, one of the methods of plotting the graph is using its slope and $ y $ - intercept method. Otherwise we can use tables to find out for which value of one variable, the other variable satisfies the equation. Plot the values in that table and join the points to give the graph of that linear equation.

Complete step-by-step answer:
Firstly we need to confirm what the linear equation given is;
Note that down:
 $ - x + 2y = 1 $
Keeping only one variable on each side;
 $ 2y = x + 1 $
Isolate the variable on the left hand side;
 $ y = \dfrac{{x + 1}}{2} $
Now that we have the isolated variable $ y $ on the left hand side, we can give $ x $ several values and find the corresponding result for $ y $
Using the points for $ x $ and $ y $ , taking them as the coordinates, we can plot the graph.
Let us move us to make a table for $ x $ and $ y $ , where we give a value to $ x $ and find the value of $ y $ :

$ x $	$ y $
$ 0 $	$ 0.5 $
$ - 1 $	$ 0 $
$ 3 $	$ 2 $

Since we have got a few values for variables $ x $ and $ y $ , we can go ahead and plot them;
We plot it in this manner;
- We first plot the value in the $ x $ column on the $ x $ - axis. Then we plot the corresponding $ y $ value from the next column onto the $ y $ - axis.
- Do the same for each of the following values and join the points, after that your plot of this linear equation should look like this;

Note: Another easy way of plotting a linear graph for any linear equation is by slope method. This we do so by first finding the intercepts for the variables, by finding the value of one variable by keeping the other as $ 0 $ . Then the coordinates will come as $ (0,y) $ and $ (x,0) $ , plot those points and when we join the line we get the graph for the linear equation.