Question

Graph the following inequalities4x + y ≥ 0

Answer 1

Solution:

Given:

$4x+y\ge0$

To get the inequality graph, we first assume the inequality to be an equation.

Hence,

4x + y = 0

Since the equation is a linear equation, we find two points needed to plot the line.

The line of the inequality will be a bold line since the inequality sign is greater than or equal to.

Hence, to get the two points,

$\begin{gathered} \text{when x = 0,} \\ 4x+y=0 \\ 4(0)+y=0 \\ 0+y=0 \\ y=0 \\ \\ \text{Hence, the first point is (0,0)} \\ \\ \\ \text{when }x\text{ = 1,} \\ 4x+y=0 \\ 4(1)+y=0 \\ 4+y=0 \\ y=0-4 \\ y=-4 \\ \text{Thus, the second point is (1,-4)} \end{gathered}$

Using the two points to plot the graph using a graph plotter, the inequality is as shown below with the line bolded;

The graph of the inequality is;