How do I Graph y < 4x + 2
We draw the boundary line which has the equation that is
like the inequality except that it has an equal sign instead
of a "<".
Boundary line's equation is y = 4x + 2.
Letting x = 0, we get y = 4(0) + 2 = 2, so (0,2) is a point on the line.
Letting x - -1, we get y = 4(-1) + 2 = -2, so (-1,-2) is a point on the line.
We plot those and draw a dotted line through them, dotted because
the solution set does not include its boundary line, since the
inequality is <, and not <.
Then we pick a test point not on the line. We can pick (0,0) since
it is not on the line. We test to see if (0,0) is a solution or not.
We substitute it in the original inequality:
y < 4x + 2
0 < 4(0) + 2
0 < 2
That is true, so all the solutions are on the same side of the
boundary line that the origin is on, so we shade that side of the line:
Edwin
