1. Identify the boundary line: The inequality is y < (1/2)x - 5. The boundary line is the equation y = (1/2)x - 5.
2. Graph the boundary line: Since the inequality is strict (<), graph the line y = (1/2)x - 5 as a dashed line.
3. Find two points on the line: When x = 0, y = -5. When x = 10, y = 0. Plot these points (0, -5) and (10, 0) and draw the dashed line through them.
4. Choose a test point not on the line: The origin (0, 0) is a convenient test point.
5. Substitute the test point into the inequality: Substitute x=0 and y=0 into y < (1/2)x - 5, which gives 0 < (1/2)(0) - 5, simplifying to 0 < -5.
6. Evaluate the test: The statement 0 < -5 is false.
7. Shade the correct region: Since the test point (0, 0) does not satisfy the inequality, shade the region that does NOT contain the test point. This is the region below the dashed line y = (1/2)x - 5.
Parent Tip: Review the logic above to help your child master the concept of inequalities in two variables worksheet.
