Question

Write an inequality for the graph.

Answer 1

The answer to your question is:

The inqualites are y > -x + 6 and y > x - 4

Explanation:

Data

Look for the equations of the lines

First line

A (5, 1)

B (0,6)

m = (6 - 1) /(0 - 5)

m = 5 / -5

m = -1

y- y1 = m(x - x1)

y - 1 = -1(x - 5)

y -1 = -x + 5

y = -x + 5 + 1

y = -x + 6 The shadow are is upward the line then

y > -x + 6

Second line

A (5, 1)

B (6, 2)

m = (2 - 1) / (6 - 5)

m = 1 / 1 = 1

y - 1 = 1(x - 5)

y = x - 5 + 1

y = x - 4 The shadow must be upward the line, then

y > x - 4

Answer 2

`y\geq |x-5|+1`

Explanation:

From the graph it is clear that it is a V-shaped curve. So, the given graph represents an absolute value function.

The vertex form of an absolute function is

`y=|x-h|+k`

where, (h,k) is vertex.

The vertex of the given graph is (5,1). So the related equation of the graph is

`y=|x-5|+1`

Related line is a solid line and shaded region lie above the line, So the sign of inequality must be ≥.

`y\geq |x-5|+1`

Check by (0,0).

`0\geq |0-5|+1`

`0\geq 6`

It is a false statement.

Therefore,
`y\geq |x-5|+1`.