Question

graph the following inequality. - 2x - 2y > - 2 use the graphing tool to graph the inequality. click to enlarge graph

Explanation:

Step1: Simplify the inequality

Divide both sides of $-2x - 2y>-2$ by $- 2$. Remember to reverse the inequality sign when dividing by a negative number. We get $x + y<1$.

Step2: Rewrite in slope - intercept form

Rewrite $x + y<1$ as $y<-x + 1$. The boundary line is $y=-x + 1$, which has a slope of $-1$ and a $y$-intercept of $1$.

Step3: Determine the boundary line type

Since the inequality is $y<-x + 1$ (not $y\leq -x+1$), the boundary line $y=-x + 1$ is a dashed line.

Step4: Test a point

Choose a test - point not on the line, say $(0,0)$. Substitute $x = 0$ and $y = 0$ into the inequality $y<-x + 1$. We have $0<0 + 1$, which is true. So, we shade the region that contains the point $(0,0)$.

To graph:

1. Plot the $y$-intercept at the point $(0,1)$.
2. Use the slope of $-1$ (down 1 unit and right 1 unit) to find another point on the line, say $(1,0)$.
3. Draw a dashed line through the points $(0,1)$ and $(1,0)$.
4. Shade the region below the dashed line.

Answer:

Graph a dashed line $y=-x + 1$ and shade the region below the line.