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

Question

Abigail Allen · Accepted 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#.

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.

Savannah Anderson · Answer

undefined To graph the inequalities y ≥ 2x and y ≤ -x + 2:

1. For y ≥ 2x:
   - Plot the line y = 2x. It has a slope of 2 and passes through the origin (0,0).
   - Since it's a "greater than or equal to" inequality, the region above the line (including the line itself) is shaded.

2. For y ≤ -x + 2:
   - Plot the line y = -x + 2. It has a slope of -1 and a y-intercept of 2.
   - Since it's a "less than or equal to" inequality, the region below the line (including the line itself) is shaded.

3. The solution to the system of inequalities is the region where both shaded areas overlap.

4. Combine the shaded regions to obtain the graph of the system of inequalities.