Question

Check whether \((0,0)\) is a solution. Then sketch the graph of the inequality. $$ x+y>3 $$

Short answer

(0,0) is not a solution to the inequality \(x + y > 3\). The graph of this inequality is a dashed line for \(y = -x + 3\) and the area above this line, which includes all points (x,y) with \(x + y > 3\).

Step-by-step solution

Check if (0,0) is a solution

Substitute the coordinates of the point into the inequality: \(0+0 > 3\), which simplifies to \(0 > 3\). This is not true, so the point (0,0) is not a solution.

Sketch the graph of inequality

First, it is necessary to treat the inequality \(x + y > 3\) as an equation and graph the line \(x + y = 3\). This essentially means rearranging the equation to a more standard form \(y = -x + 3\). This line crosses the y-axis at the point (0,3) and the x-axis at the point (3,0). Use these points to draw the line. As the inequality is '>', this means that the solutions to the inequality are not on the line but in the area above it. Therefore, graph the line using a dashed line.

Indicate solution area

The area above the line \(x + y = 3\) is the solution to the inequality \(x + y > 3\). It represents all pairs of values (x,y) that satisfy the inequality. This area should be shaded on the graph.