## Precalculus (6th Edition) Blitzer

Let us consider the inequalities $x-2y<8$; substitute the equals symbol in place of the inequality and rewrite the equation as given below: By finding any two solutions of the linear equation, plot the graph of the linear equation $x-2y=8$: To find the value of the x-intercept, substitute y = 0 as follows: \begin{align} & x-2\left( 0 \right)=8 \\ & x=8 \\ \end{align} To find the value of the y-intercept, substitute x = 0 as follows: \begin{align} & 0-2y=8 \\ & y=-4 \\ \end{align} Plot the intercepts $\left( 8,0 \right)\text{ and }\left( 0,-4 \right)$ and draw a dotted line passing through these points because the inequality does not contain the equal symbol. Now this dashed line divides the plane in 3 region: the line itself, and the two half planes. Now, take the origin $\left( 0,0 \right)$ as a test point and check the region in the graph to shade: Check if the test point satisfies the inequality. $x-2y<8$ $0-2*0<8$ $0<8$ This is true, so the origin is included. See the final graph below.