Question

Where should the linear inequality y < 1/4x - 3 be shaded?

A) Above the line
B) Below the line
C) On the line
D) None of the above

Answer 1

For the linear inequality y < 1/4x - 3, a dashed line is drawn for y = 1/4x - 3, and the region below the line is shaded since the inequality symbol is '<', which excludes the equality on the boundary line.

Step-by-step explanation:

The linear inequality in question is y < 1/4x - 3. When graphing a linear inequality, we first graph the equation as if it were an equality, in this case, y = 1/4x - 3. This line will serve as the boundary for the inequality. For linear inequalities like the one given, we use a dashed line to represent the boundary when the inequality is strict (<, >), which means the values on the line itself are not included in the solution.

To determine where to shade the graph, you can pick a test point that is not on the line. A common choice is the origin (0,0) if it's not on the line. If the inequality is true when you plug in the coordinates of the test point, then you shade the side of the line where the test point lies. If not, you shade the opposite side. Since y < 1/4x - 3, if we plug in (0,0), we get 0 < -3, which is false, so we shade the side opposite to where the point (0,0) lies, which is below the line.