Question

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

Short answer

Yes, the point (0,0) is a solution to the inequality \(3x - y < 3\). The graph of the inequality is a dashed line along \(y = 3x\), with shading in the region below the line.

Step-by-step solution

Test the solution

Substitute x=0 and y=0 into the inequality, \( 3x - y < 3 \). If the inequality holds true, then (0,0) is a solution.

Solve inequality

After substituting, the inequality is 3(0) - 0 < 3, which simplifies to 0 < 3. Since this inequality is true, the coordinate point (0,0) is a solution to the original inequality.

Sketch the graph

First rewrite the inequality in y = mx + b form, where m is the slope and b is the y-intercept, by adding y to both sides gives \(3x < 3 + y\). Then convert the inequality to an equation \(3x = y + 3\) for graphing. Graph this line on the Cartesian plane. Because the inequality is ''less than'' and not ''less than or equal to'', the line on the graph should be dashed or dotted. Next, choose a random point not on the line (like (0,0)), if it makes the inequality true, shade the side of line where point lies, otherwise shade the opposite side.