graph the inequalities y>2x+1

Question

graph should have a table of values used to graph and label the vertex if an absolute value inequality.

Answer 1

pretend for one moment it is an equation..

y = 2x+1

it is a line with y-intercept (0,1) and slope 2.

so plots (0,1). Then goes up 2 and 1 to the right,

which is (1,3)

Now, since it is actually an INEQUALITY, you draw

the line with dotted/dashed line.

Finally, testing the origin (0,0):

0 > 2(0) + 1

0 > 1 is FALSE

so shades ABOVE the line AWAY from the origin

any point above this line will work and result

in a true statement when substituted.

any point BELOW this line (like the origin)

will fail and result in a FALSE statement when substituted.

For example, (0,5) is in the solution region...

5 > 2(0) + 1 = 1 is true

vs.

(0,-5) which results in -5 > 2(0) + 1 --> -5 > 1 if FALSE