Which point is a solution to the linear inequality y < negative one-halfx + 2?

The solution in the attached figure

see the explanation

Step-by-step explanation:

we have

The solution of the inequality is the shaded area below the dashed line

The slope of the dashed line is negative

The y-intercept of the dashed line is the point (0,2)

The x-intercept of the dashed line is the point (4,0)

using a graphing tool

The solution in the attached figure

Remember that

Any point that lie on the shaded area is a solution of the inequality and if a point is a solution of the linear inequality, then the point must satisfy the inequality

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

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