Question

Check whether \((0,0)\) is a solution. Then sketch the graph of the inequality. $$ x+y<4 $$

Short answer

The point (0,0) is indeed a solution to the inequality 'x+y<4'. When the inequality 'x+y<4' is graphed, the solution region is the area below the line 'x+y=4'.

Step-by-step solution

Verify if given point is a solution

Substitute the coordinates of the given point (0,0) into the inequality 'x+y<4'. If the inequality becomes true after substitution, then we can say that the given point is a solution. Substituting (0,0) into 'x+y<4', we get '0+0<4', which is true. Hence, (0,0) is a solution for the inequality 'x+y<4'.

Plot the inequality

From the inequality 'x+y<4', it can be seen that the line dividing the solution region from the non-solution region in the graph is 'x+y=4'. Plot this line on a two-dimensional graph with x and y axes. This line intersects the y-axis at (0,4) and the x-axis at (4,0). Draw this line on graph.

Shade the solution region

Since we have found out that (0,0) is a solution for the given equation, and it lies below the line 'x+y=4', we shade the region below this line on the graph. The shaded region represents the solution for the inequality 'x+y<4'.