Question

Draw the graph for each of the equations \[x + y = 0\] and \[x - y = 2\] on the same graph paper and find the coordinates of the point where the two straight lines intersect.

Answer 1

Hint:
Here we are given two equations that are \[x + y = 0\] and \[x - y = 2\] also we are asked to plot these equations graph on the graph paper and also we are asked to find the coordinates of the points where the two straight lines intersect .For this we need to first plot the graph for which we have to find the points first which satisfy these equation and later on plotting these points on the graph paper and checking where the two straight lines \[x + y = 0\]and \[x - y = 2\] intersect .

Complete step by step solution:
Here we are given two equations \[x + y = 0\] and \[x - y = 2\] for which we are asked to draw the graph and also find the coordinates of the point where the two straight lines intersect
So firstly for drawing the graphs of the equation \[x + y = 0\] and \[x - y = 2\] we need to find the coordinates of \[x\] and \[y\] which satisfy the equations \[x + y = 0\] and \[x - y = 2\]
Now finding the coordinates for the graph of the equation \[x + y = 0\]
Putting \[x = 5, 10 \text{and} 15\] in the equation \[x + y = 0\] the coordinates of \[y\] will be \[ - 5, - 10 \text{and} - 15\]
Here the table of the coordinates for the equation\[x + y = 0\] will be –

Now for the equation \[x - y = 2\] finding its coordinates for the graph
Putting \[x = 1,7{\text{ }}and{\text{ - 8}}\] in the equation \[x - y = 2\] the coordinates of \[y\]will be \[y = - 1,5{\text{ }}and{\text{ - }}10\]
Here the table of the coordinates for the equation \[x - y = 2\] will be-

Now plotting the resultant coordinates we get the graph of the equations \[x + y = 0\]and \[x - y = 2\] that is-

Here we can see in the graph clearly that the two equations \[x + y = 0\] and \[x - y = 2\]intersect at the point \[\left( {1,1} \right)\]
So the coordinates of the point where the two straight lines formed by the equations \[x + y = 0\] and \[x - y = 2\] intersect at are \[\left( {1,1} \right)\]

Note:
While approaching these kinds of questions (graph related questions) the coordinates found through the given equations in the question should be plotted with precision to get the right form of the graph and which helps in finding the point of the intersection easily and correctly.