Answer
The wanted region which is the solution of these two given inequality equations is the region further to the left, in yellow.
Step-by-step explanation
To plot graphs for inequalities, it involves plotting the straight line graphs of the given equations and shading the wanted regions.
If the inequality sign is (≤ or ≥), the line of the graph will be a thick, unbroken line.
But if the inequality sign is (< or >), the line of the graph will be a broken line.
So, the two equations to be plotted are
y > 2x + 4
x + y ≤ 6
The first step is to write both equations in the standard form of the equation of a straight line, y = mx + c, although, since this is an inequality graph, the equal to sign (=) in the standard form will be replaced by an inequality sign.
The first equation is already in the required form, but we will need to put the second equation in the required form
y > 2x + 4
y ≤ -x + 6
So, the next step is to plot the equation of the two straight lines on the same graph
y = 2x + 4
y = -x + 6
Recall what I said about broken lines and thick lines.
So, the graph of y > 2x + 4 will be a broken one, and with the inequality sign saying that y is greater than 2x + 4, the wanted region will be the parts above the broken straight line, marked all in red.
The graph of y ≤ -x + 6 will be an unbroken thick one, with the inequality sign dictating that y is less than or equal to -x + 6, the wanted region will be the parts below the unbroken, thick straight line, marked in green.
The solution of this graph will then be the region of intersection of the region marked green and the regions marked red.
The wanted region which is the solution of these two given inequality equations is the region further to the left, in yellow.
Hope this Helps!!!