Two Variable Inequalities
MAT 222 Intermediate Algebra
Instructor Leah Murray
November 4, 2013
TWO VARIABLE INEQUALITIES
For this assignment, I am going to work with two-variable inequalities and demonstrate the practical application of these inequalities. I am going to use a graph that shows the number of TV’s on the left side and the number of refrigerators on the bottom. Of course this would mean that my x axis is the bottom, and my y axis on the left. The line shows the combination of TV’s and refrigerators that the truck can hold.
The problem I am going to work on is #68 on page 539 . The
18 wheeler truck can hold 330 TV’s with no refrigerators, or 110 refrigerators and no TV’s. When studying this graph, imagine that the triangle region is shaded, and that it represents any given number of coordinates that is in the shaded area is a combination of TV’s and refrigerators that will fit in the truck.
Because there are two points on the graph, I can figure out the slope of the line. So our slope is -3/1
I can now use this slop in point-slope form to write an equation. When we are finished, we will arrive at our linear inequality.
Our point-slope form equation
Replace the slope with-3/1 and (330,0) for the x and y
Add 330 to both sides using the distributive property
Multiply both sides by 1, then add 3x to both sides
Change the equal sign to a less than or equal to symbol. Because the line represents coordinates that can include numbers on that line, as well as anything in the shaded part, we will use a solid line, instead of a dotted line. This is also represented in the symbol having the equal bar underneath the less than symbol.
Now I am going to answer the two questions that accompany the first part of the assignment.
The first question asks if the truck will hold 71 refrigerators and 118 TV’s. Another way to phrase this is to ask if the coordinates...
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