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

Jun 28, 2017

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 $y = 2 x$.

#### 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 $y = 2 x$. As the inequality is $\ge$, 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 $\le$, 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:
$y = 2 x$:
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.