How do you graph the inequality #y≥2x# and #y ≤-x+2#?

1 Answer

Draw a solid line for the lones of the two equations, and shade under the area of the graph for the equation #y=-x-2#, and shade above the area of the graph for the equation #y=2x#.

Explanation:

Not much of an explanation here, but draw two graph.

On one graph draw a solid line, not dashed, of gradient 2, rhe goes through the origin, and label it #y=2x#. As the inequality is #>=#, you want all parts of the graph above the line, this is done by shading the area on your graph above said line.

On your secnd graph, draw a solid line of gradient -1, and a y-intercept of 2 and label it #y=-x+2#. As the inequality is #<=#, you want all parts of the graph below the line, this is done by shading the area on your graph below said line.

Graphs for reference:
#y=2x#:
graph{2x [-10, 10, -5, 5]}

#y=-x+2#:
graph{-x+2 [-10, 10, -5, 5]}

and solution is given by all points in the shaded region, as it satisfies both the inequalities. The points on the lines are also included.
enter image source here