Question

Write an inequality for the graph.

Answer 1

Answer:

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

Step-by-step 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, $y\geq |x-5|+1$.

Answer 2

Answer:

The answer to your question is:

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

Step-by-step 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