Question

Write an inequality for the graph.

Answer 1

This is the Graph

Answer 2

The boundary line is an absolute value equation

Answer 3

The general absolute value equation is

y = a|x-h| + k

where (h,k) is the vertex

Answer 4

What is the vertex here?

Answer 5

idk...

Answer 6

look at the lowest point (where the sharp pointy end is)

Answer 7

what is that point?

Answer 8

5/1

Answer 9

good, it's (5,1)

So h = 5 and k = 1

Answer 10

This means that

y = a|x-h| + k

becomes

y = a|x-5| + 1

Answer 11

ok

Answer 12

Now plug in another point, say (4,2), and solve for 'a'

y = a|x-5| + 1

2 = a|4-5| + 1

2 = a|-1| + 1

2 = a(1) + 1

2 = a+1

2-1 = a

1 = a

a = 1

So the equation of the boundary line is

y = 1|x-5| + 1

which simplifies to

y = |x-5| + 1

Answer 13

Where is the shaded region? Above or below the boundary line?

Answer 14

above

Answer 15

the boundary line is also solid

Answer 16

so we use the \(\Large \ge\) sign

this means that the inequality shown is

\[\Large y \ge |x-5|+1\]

Answer 17

Thx alot :D <3

Answer 18

you're welcome