Question

Determine the type of boundary line and shading for the graph of the inequality 4x + y > -6.

Answer 1

Determining the boundary line is easily accomplished by replacing the > symbol with =. Solve the resulting equation for y in terms of x: y = m*x + b. The slope of this boundary line will be m and the y-intercept will be b. Graph it using a dashed or dotted (not solid) liine (because you're dealing with an inequality here).

Now pick any point on the xy plane which is NOT on the boundary line. Substitute the coordinates of that point into the original inequality. The resulting inequality will be either true or false. If true, shade the side of the boundary line from which your point came. If false, shade the other side.

For example, test the point (1, 2). Here x = 1 and y = 2.
What happens if you substitute those values into the original inequality?

Answer 2

Now test the point (1,3). Here x = 1 and y = 3. How is the result different from before?