A linear inequality in and marks a region of valid points, not just a line. If a question asks which table contains only valid points, graph the inequality in Desmos and test the rows as ordered pairs. One point outside rules out its table, but you must check every point in the table you keep. Don’t stop after finding one row that works.
Hints
- Hint 1
The boundary line is where the two sides of the inequality are equal. The symbol means can be on or below that line. Which side does Desmos shade when you enter the inequality?
- Hint 2
An ordered pair gives first and second. Because a table must contain only solutions, a single point above the line rules out that whole table. Look for a quick row to test in each.
- Hint 3
After ruling out tables, check every row of the one left. A point on the boundary line counts because includes equality, but a point above the line does not.
Step-by-step
Graph the inequality and test the rows
Step 1Find the allowed region
Type into Desmos. It shades on and below the boundary line, where the two sides are equal. The line is solid because allows equality.
- Step 2
Rule out tables with a failing row
Plot , , and , using the first column for and the second for . Desmos shows all three above the shading. They come from three different tables; is the second row of its table, so checking its first row alone would miss it. One failing row rules out the whole table.
- Step 3
Check every row of the remaining table
Plot , , and from the remaining table. Desmos places all three in the shaded region, so every row satisfies the inequality. That table contains only valid pairs. Choice C.