linear inequalities n graphing?

To begin with you have to graph the solutions of 4 inequalities. If you can graph one; you can graph four repeating the same steps 3 more times.

Use a full page of math paper to graph clean graphs and get accurate information.

What you called part a) and part b) are not correct, if you write a function 2x - y ,it has to be equal to something like 2x - y = 0 , or another number. I assumed the both were equal to zero.

To graph one inequality do the following:( I am going to do y< 1/2 x + 3 )

a) Write the equation of the critical line:

........... y = 1/2 x + 3 ........................ Just change < or > for =

b) Find two solutions to be able to graph the line:

.... For example when x= 0, then y= 3 and the solution is ( 0, 3)

.... Next make x= 2 and y will be 4, the second solution is ( 2, 4)

c) Graph the 2 points from b) and using a ruler draw the line through the two points.

d) Now choose a " Test Point " to identify the side of the line that has the "True Points "

e) Whenever possible choose the point (0,0 ) . The origin.

f) Replace x by 0 and y by 0 in the Original Inequality " and simplify:

..... 0 < 1/2 (0) + 3 ................... Simplify

......0 < 3 TRUE.

g) That means that the side of the line where ( 0,0) is has the TRUE solutions, shade it lightly ( Use pencil )

Repeat the steps from a to g for the other 3 inequalities.

At the end of the fourth one , you will have a triangular region shaded 4 times.

Next draw ( with blue ink ) the line that represents the function in part (a), after you have corrected it.

To graph the line ,do the same as in parts (b) and (c) of the process. ( You do not have to do parts

d, e, and f because it is not an inequality )

Check where the line for your part a) crosses the upper side of the triangular region. It should be at the point ( 2, 4 ). The y value, y= 4 is the highest value the function takes is that region .

Repeat for your part b) check at what point the line for part b) crosses the lower side of the triangular region, since we are looking for the least or minimum, in this case it looks like it is the point (0,0 ) . So the minimum value will be zero.

I assumed that that two functions were equal to zero.

As you can see, the process is not difficult, but long and tedious, you have to be neat, and make a big graph.

Have fun.