why isn't the answer just one point or just one line when graphing inequalities
Because the answer can equal more or less than the line that was graphed
When graphing inequalities, we use different symbols and shading to represent the range of possible solutions. This is because the answer to an inequality can include not only the line itself, but also any values above, below, to the left, or to the right of the line.
Let's consider a simple example: the inequality y > 2x. If we were to graph this inequality, we would start by drawing the line y = 2x. However, this line itself is not the answer. It simply serves as a boundary or reference point.
To identify the specific region that satisfies the inequality, we need to determine whether the solution includes the area above or below the line. In this case, since the inequality states y > 2x, the solution should include all the points above the line. To represent this, we typically shade the region above the line to indicate that it satisfies the inequality. This shading indicates that any point in that area will make the inequality true.
On the other hand, if the inequality were y < 2x, we would need to shade the region below the line, because any point in that region would satisfy the inequality.
By using shading and symbols like "greater than" (>), "less than" (<), "greater than or equal to" (≥), or "less than or equal to" (≤), we can accurately represent the range of values that satisfy the inequality. This allows us to show that the solutions to an inequality can extend beyond a single point or line on the graph.