Question

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?

Answer 1

Step-by-step explanation:

y≤

3

2x

+

5

1

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 ,

(y-y2)=\frac{y1-y2}{x1-x2}*(x-x2)(y−y2)=

x1−x2

y1−y2

∗(x−x2)

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

\begin{gathered}y-0.2=\frac{2.2-0.2}{3-0}*(x-0 )\\2x-3y+0.6=0\end{gathered}

y−0.2=

3−0

2.2−0.2

∗(x−0)

2x−3y+0.6=0

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.

y\leq \frac{2x}{3}+\frac{1}{5}y≤

3

2x

+

5

1