Question

How do you graph $ y=x-10 $ ?

Answer 1

Hint: To draw the graph of the above equation $ y=x-10 $, we are going to put $ x $ as 0 and then will see what values of y we are getting. Then plot these x and y coordinates on the graph paper. After that, we are going to put $ y $ as 0 in the above equation and see what values of $ x $ we are getting and then plot these x and y coordinates on the graph paper. Now, join these two points to get the straight line.

Complete step by step answer:
In the above problem, the equation of a straight line that we are given is as follows:
 $ y=x-10 $
Now, we are going to substitute the value of $ x $ as 0 in the above equation.
 $ \begin{align}
  & y=0-10 \\
 & \Rightarrow y=-10 \\
\end{align} $
Hence, we got the point $ \left( 0,-10 \right) $ from the above calculations. Now, we are going to plot this point on the graph paper.

Now, we are going to substitute y as 0 in the above equation.
 $ \begin{align}
  & \left( 0 \right)=x-10 \\
 & \Rightarrow x=10 \\
\end{align} $
From the above, we got the second point whose x and y coordinates as (10, 0). Let us draw this point (10, 0) on the graph paper and we get,

Now, to draw the equation of a straight line we are going to join these two points.

Hence, from the above, you can see that we have drawn the equation given in the above problem on the graph.

Note:
 We can check whether the straight line that we drew is correct or not by taking a point on the straight line whose x coordinate is 5 and then to know the y coordinate of that point we are going to draw a perpendicular from this point on to the y axis. The foot of the perpendicular is the coordinate of the y-axis of that point.

From the above, as you can see that the foot of the perpendicular from point C is at -5 which is the y coordinate of point C.
Now, we can check whether the y coordinate of point C is 5 or not. Let us substitute the x coordinate as 5 in the above equation we get,
$\begin{align}
  & y=\left( 5 \right)-10 \\
 & \Rightarrow y=-5 \\
\end{align}$
From the above, we are getting the same value of y which we got from the graph. Hence, the graph that we drew corresponding to the given equation is correct.