1. The point (0, ½) is a solution because substituting x=0 and y=½ into the equation gives 2(½) - 0 = 1, which simplifies to 1 = 1. The point (-7, -3) is also a solution because substituting x=-7 and y=-3 gives 2(-3) - (-7) = -6 + 7 = 1, which simplifies to 1 = 1.
2. For (0,2): 2(2) - 0 = 4 > 1 → yes.
For (8, ½): 2(½) - 8 = 1 - 8 = -7 > 1? No.
For (-6,3): 2(3) - (-6) = 6 + 6 = 12 > 1 → yes.
For (-7,-3): 2(-3) - (-7) = -6 + 7 = 1 > 1? No.
3. Shade the region above the line 2y - x = 1, since the inequality 2y - x > 1 represents all points where the expression is greater than 1, which corresponds to the area above the line.
4. Points on the line are not included in the solution set because the inequality is strict (>) and does not include equality. Only points strictly above the line satisfy 2y - x > 1.
Parent Tip: Review the logic above to help your child master the concept of algebra 1 8 6.
