The linear inequality
represents a half-plane above the line
. Points in this shaded region satisfy the inequality, with the line itself not included due to the strict inequality (
). Hence, graph 2 is correct.
The linear inequality
represents a half-plane above the line
. The inequality indicates that any point (x, y) above the line satisfies the inequality.
The line itself is not included in the solution, as the inequality is strict (
). The slope of the line is
, meaning it goes downward from left to right.
The y-intercept is 5, and the line extends infinitely in both directions. Shading the area above the line represents the solution region for
.
Any point in this shaded region, when substituted into the inequality, will result in a true statement, satisfying the inequality. The graph 2 given shows the linear inequality y > -4/3x + 5.