Question

For this linear inequality, describe how to represent the solutions on a graph:

y< 2x+5
O check all solutions to see if they make true statements
O shade to the left of the boundary
shade below the boundary line
O shade above the boundary

Answer 1

Answer / Step-by-step explanation:

To represent the solutions of the linear inequality y < 2x + 5 on a graph, we can follow these steps:

First, we draw the boundary line y = 2x + 5, which is a straight line with a slope of 2 and a y-intercept of 5.

Since the inequality is y < 2x + 5, we need to shade the region that is below the boundary line. This is because any point below the line will have a y-coordinate that is less than 2x + 5, which satisfies the inequality.

We can also use a dashed line to represent the boundary line, since the inequality is strict (y < 2x + 5, not y ≤ 2x + 5).

Finally, we can check the solutions to the inequality by picking any point in the shaded region and plugging its coordinates into the inequality. If the resulting statement is true, then that point is a valid solution to the inequality. If the statement is false, then the point is not a solution.

Therefore, to represent the solutions of the inequality y < 2x + 5 on a graph, we would shade below the dashed line y = 2x + 5.