Question

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

Answer 1

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.