Question

Draw the graph of the equation \[y - x = 2\]

Answer 1

Hint: We plot the graph of the given equation by substituting values of x and calculating the simultaneous value of y one by one. We firstly calculate the x and y intercepts and plot the points on the graph.
* Intercept means the point where the line crosses the respective axis. So, x-intercept means the point on x-axis where the line cuts the x-axis and y-intercept means the point on y-axis where the line cuts the y-axis.

Complete step-by-step solution:
We are given an equation in two variables ‘x’ and ‘y’.
Equation in two variables is \[y - x = 2\] … (1)
We can either substitute value of ‘x’ and calculate value of ‘y’ or we can substitute value of ‘y’ and calculate value of ‘x’.
X-intercept:
X-intercept of a line means the point on x-axis where the line cuts the x-axis. So the value of y-coordinate is 0 at the x-intercept.
Put \[y = 0\] in equation (1)
\[ \Rightarrow 0 - x = 2\]
\[ \Rightarrow - x = 2\]
Multiply both sides of the equation by -1
\[ \Rightarrow - x \times ( - 1) = 2 \times ( - 1)\]
\[ \Rightarrow x = - 2\]
So, the point becomes \[( - 2,0)\]
Y-intercept:
Y-intercept of a line means the point on y-axis where the line cuts the y-axis. So the value of x-coordinate is 0 at the y-intercept.
Put \[x = 0\] in equation (1)
\[ \Rightarrow y - 0 = 2\]
\[ \Rightarrow y = 2\]
So, the point becomes \[(0,2)\]
Now we plot x-intercept \[( - 2,0)\] and y-intercept \[(0,2)\] on the graph and join the straight line joining the two points.

So, the graph of the equation \[y - x = 2\] is represented above.

Note: Students many times do long calculations and calculate many points by substituting values of x or y in the equation. Keep in mind we only need two points on the graph to plot a line as the line is always a straight line. So using a ruler we can join any two points on the graph. It is always easier to calculate the intercepts as one of the coordinate values is 0.