On a coordinate plane, a solid straight line has a positive slope and goes through (0, 0.2) and (3, 2.2). everything to the right of the line is shaded.
which linear inequality is represented by the graph?

y > two-thirdsx – one-fifth
y ≥ three-halvesx + one-fifth
y ≤ two-thirdsx + one-fifth
y < three-halvesx – one-fifth

Step-by-step explanation:

It is given that we have a line equation from (0,0.2) to (3, 2.2) with positive slope.Firstly for calculating the line equation between two points (x1,y1),(x2,y2) we have the relation ,

In the given case substituting them we get the line equation as

The condition was that everything to the right of the curve is shaded.

This is an inequality which needs to be solved with boundary conditions.

We notice that for x to the right of the equation y is always less than the existing line.(As it has a positive slope)

So for all x greater than or to the right of the line y lies below the line.

c)

Step-by-step explanation:

Given points:

and

Finding slope:

Using point intercept equation to find equation of line:

Simplifying to standard form by adding 0.2 to both sides.

  [∵ ]

Now, the graph has right side shaded with the solid line. Thus we can write the inequality represented by the graph as:

[∵  represent shaded are below the line which lies to the right including the line(solid)]

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