Graphing Linear Inequalities in Two Variables
When graphing a linear inequality like 6x - 3y > 18, first rearrange it into slope-intercept form. For this example, we get y < 2x - 6 by isolating y. The boundary line is y = 2x - 6, which we draw as a dashed line since the inequality uses < (not ≤).
To determine which side of the line to shade, we need to remember some key rules. For inequalities with y > or y ≥, shade above the line. For y < or y ≤, shade below the line. When given in the form ax + by > c or ax + by < c, test a point (like the origin) to determine which region to shade.
Different types of inequalities include horizontal lines (y < 4), vertical lines , and sloped lines . Each creates different shading regions based on the inequality symbol used.
Remember this! The boundary line is solid for ≤ or ≥ inequalities (inclusive) and dashed for < or > inequalities (exclusive). This shows whether points on the line itself are part of the solution.
