Question

Does anyone want to help me with six questions on Graphing Linear and Absolute Value Equations and Inequalities?

Answer 1

@jim_thompson5910 could you help me?

Answer 2

@Luis_Rivera

Answer 3

name one

Answer 4

the most basic one is
\[y=|x|\] which looks like this

Answer 5

here is the attachment of the assignment

Answer 6

you can plot some points if you like, or maybe we can do the following
take the graph i wrote above
\[y=|x|\] then for
\[y=|x-2|\] you shift it to the right two units,
then for
\[y=-\frac{1}{5}|x-2|\] flip it up side down and make the slops of the lines \(\frac{1}{5}\) and \(-\frac{1}{5}\) instead of \(-1\) and \(1\)

then shift it up 3 units to get
\[y=-\frac{1}{5}|x-2|+3\]

Answer 7

here is a picture from wolfram
http://www.wolframalpha.com/input/?i=y%3D-1%2F5 |x-2|%2B3

Answer 8

we could also do this
make a point at \((2,3)\) which is the highest point on the graph

Answer 9

then plot a couple other well chosen points, say \(x=7\) gives you
\[y=-\frac{1}{5}|7-2|+3=-1+3=2\] so plot \((7,2)\)

Answer 10

and \(x=-3\) give you
\[y=-\frac{1}{5}|-3-2|+3=-1+3=2\] so plot \((-3,2)\)
connect the points \((2,3)\) and \((-3,2)\) with a straight line
connect the points \((2,3)\) and \((7,2)\) with another straight line

you want
\[y\geq -\frac{1}{5}|x-2|+3\] so shade everything above those two lines

Answer 11

could you do this on the assignment I attached?