Write an inequality for the graph. !

This involves interpretation of inequality on a graph.

y ≥ -x+6

y ≥ x - 4

y = mx + c

Let's start with coordinates for the line slanting rightwards.

At x = 0, y = 6

At x = 1, y = 5

Thus;

6 = 0(m) + c

c = 6

Also;

5 = 1(m) + 6

5 - 6 = m

m = -1

Thus, the equation is;

y = -x + 6

We can see the line is a broken line and the shaded portion is above the line. This represents;

y ≥ -x+6

For the second line;

At x = 5, y = 1

At x = 6, y = 2

Thus;

1 = 5m + c

2 = 6m + c

Subtract eq 1 from eq 2 to get;

m = 1

Thus;

1 = 5(1) + c

c = 1 - 5

c = -4

This represents;

y = x - 4

We can see the line is a broken line and the shaded portion is above the line. This represents;

y ≥ x - 4

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There are 2 lines, so this is a system of inequalities.

Find the equation of both lines:

The longer line using points (0,6) and (3,3)

Equation is y = -X+6, the inequality becomes y ≥-x+6

The equation for the shorter line:

Using points (5,1) and (6,2)

Equation is y=x-4, the inequality becomes y≤x-4

The system of inequalities is:

y ≥-x+6

y≤x-4