*When graphing an inequality, there are some new things compared to graphing an equation:
Solid line: use whenever “=” is involved
Broken line: use when “=” is not involved
Shade the region to indicate the true values of the inequality.
*The steps to graph an inequality:
– Identify the line or parabola that represents the equation, which is the inequality with “=” sign.
– If the inequality involves “=”, use the solid line. If it doesn’t, use broken line (dashes).
– Determine the shaded region by substitute a coordinate of a point into the inequality. If the x and value make the inequality a true statement, shade the region that comprises the chosen point, and vice versa.
For example:
Graph y > 3x + 4
-Identify the line
– Since the inequality doesn’t involve “=” sign, use broken line
– Insert (0,0) into the inequality, we have 0 > 4 -> false. Shade the other region.
Graph
– Identify the parabola
– Since the inequality involves “=” sign, use solid line.
– Insert (0,0) into the inequality, we have 
*When writing an inequality for a graph, follow these steps:
-Write an equation for the line/ parabola.
-Insert the coordinate of a point in the shaded region into the equation.
– Based on the result and the kind of line (solid or broken) to determine the suitable sign.
*There is a way to quickly determine the shaded region:
Look at the y-intercept. If the sign is “y>…”, shade the region containing points above the y-intercept. If the sign is “y<...", shade the region that contains points below the y-intercept.
This technique can be apply to both linear and quadratic inequality.
