Question

When an inequality is written in slope intercept form, the inequality symbol indicates which type of line to draw and which side to shade. List the four inequality symbols and how each one relates to the graph. For example, y< tells you that the line is ______ and the shading is _____ the line. (Rewrite the sentence with the correct word in each blank.)o

Answer 1

• (<, dashed, below)
• (>, dashed, above)
• (≤, solid, below)
• (≥, solid, above)

Explanation:

When the inequality symbol includes the "or equal to" case, the line is part of the solution set, so is drawn as a solid line. Otherwise, it is drawn as a dashed line, because it is not part of the solution set.

When the inequality symbol is < or ≤, the expression y < ... tells you that values of y in the solution set are below the line, that is, less than values that are on the line. The symbol > or ≥ in the expression y > ... tells you y-values in the solution set are greater than those on the line, so shading will be above the line.

Your statement can be filled with the triples shown above:

The inequality y [symbol] ... tells you that the line is [type of line] and the shading is [direction] the line.