Question

Draw the graph of linear equations y = x and y = x + 1 on the same Cartesian plane. What do you observe?

Answer 1

Hint: In order to make observations we make a suitable graph and plot both the equations on it. Then we check for similarities like common intercepts, intersecting points etc.

Complete Step-by-Step solution:

Given, y = x and y = x + 1.

y = x is a straight line passing through the origin at (0, 0).

y = x + 1, is a straight line as well.

From the figure, they don’t intersect.

Put y = 0, we get x = -1.

y = 1, we get x = 0.

y = 2, we get x = 1.

X = -1, 0, 1

Y= 0, 1, 2

That is at no point the values of X and Y are equal.

Thus, the lines are parallel to each other and have no solution.

Note: In order to solve this type of questions the key is to have adequate knowledge in straight lines, their graphs and their properties. To plot a graph given by an equation, we substitute random values of one variable to determine the other, we plot all such obtained points and join them by a straight line.