# Two Variable Inequality

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Two-Variable Inequality Cassie Lane MAT222 Week 2 Assignment Instructor Alvarez Guillermo February 03, 2014 Two-Variable Inequality In week 2’s assignment we will be covering practical application of two-variable inequalities. I will be covering independent and dependent variables. In the first part of my assignment I will be working out problem #68 on page 539 (Dugopolski, 2012). The problem asks about Shipping restrictions. The accompanying graph shows all of the possibilities for the number of refrigerators and the number of TVs that will fit into an 18-wheeler. a) Write an inequality to describe this region. b) Will the truck hold 71 refrigerators and 118 TVs? c) Will the truck hold 51 refrigerators and 176 TVs? To better help you follow my work I will start out with the question as seen above as part 1 and for the other questions that I was asked to do by my instructor as part 2. Part 1 (a) Write an inequality to describe this region. In our book it shows a graph stating the two points so that we can find our slope. The points are (0,330) and (110, 0). The slope is m=y1-y2x1-x2=0-330110-0=-31 So the slope is -31 The point-slope form of a linear equation to write the equation itself can now be used. These are the steps we take to arrive at our linear inequality. y-y1=m(x-x1) Slope point form y-330=-31(x-0) Substitute the slope for m and (330, 0) for the x and y. y-330+330=-31x-0+330 Use distributive property and then add 330 to both sides. y=-31x+330 y×-3=-31x+330×-3 Multiply both sides by -3 3x+y ≤ 990 Add -3 to both sides and change to less than or equal to symbol The graph has a solid line rather than a dashed/dotted line indicating that points on the line itself are part of the solution set. This will be true anytime the inequality symbol has the equal to bar. There are two