Mathematics
Mathematics
Problem
For the inequality , answer the following: a. (i) Determine the –intercept and –intercept of its boundary line. b. (ii) State whether the boundary line should be solid or dashed. c. (iii) Decide whether the origin lies inside the solution region of the inequality.Intuitive explanation
The key to graphing a linear inequality is to first treat it like an equation to find the boundary line, then use a test point to determine which side of that line satisfies the inequality. Since the inequality is strict (>), the boundary itself won't be included—you'll use a dashed line. The real insight is that one entire half-plane will be your solution, so pick any point not on the line to see which region works.
Intuitive explanation
The key to graphing a linear inequality is to first treat it like an equation to find the boundary line, then use a test point to determine which side of that line satisfies the inequality. Since the inequality is strict (>), the boundary itself won't be included—you'll use a dashed line. The real insight is that one entire half-plane will be your solution, so pick any point not on the line to see which region works.