Two-Variable Inequalities
Two-Variable Inequalities
Kathleen Kent
MAT 222 Week 2 Assignment
Guillermo Alvarez
September 22, 2014
Two-Variable Inequalities
This week’s assignment will show how two-variable inequalities can be used in real-world scenarios by using independent and dependent variables. This week’s assignment will use graph representations and show how the two-variable inequalities can be incorporated into several problems to show how many of each item trucks can ship without going over their weight limit.
The first problem that I will be doing is #68 on page 539 (Dugopolski, 2012). Below, the graph shows the maximum number of TVs the 18-wheeler can hold without refrigerators, and the maximum number of refrigerators the 18-wheeler can hold without TVs.
On the X-axis, the graph shows the refrigerators, and on the Y-axis, the graph shows the TVs that the 18-wheeler can carry at a time. To find the slope of the line, I will use the two points that are on the graph, (0,330) and (110,0).
The slope is m= y1 - y2 = 0 – 330 = -330 = -3, so the slope is -3. x1 – x2 110 – 0 110
To make it easier to find how many refrigerators and how many TVs can fit in the 18-wheeler, it would be best to have a linear equation. To find the linear equation, the point-slope form can be used. y - y1 = m(x – x1) This is the point-slope form. y – 330 = -3 (x - 0) The slope is substituted for m and (330,0) is substituted for x and y. y = -3x + 330 Distributive property is used and 330 is added to both sides. y+3x ≤ 330 3x is added to both sides and the less than or equal to symbol has been changed.
The graph shown above has a solid line instead of a dotted line because the points that are on the line are a part of the solution set. Anytime the inequality symbol has the “equal to” bar, the line will be solid rather than dotted.
There are two more parts to problem #68 on page 539.
1. Will the truck hold 71 refrigerators
Kathleen Kent
MAT 222 Week 2 Assignment
Guillermo Alvarez
September 22, 2014
Two-Variable Inequalities
This week’s assignment will show how two-variable inequalities can be used in real-world scenarios by using independent and dependent variables. This week’s assignment will use graph representations and show how the two-variable inequalities can be incorporated into several problems to show how many of each item trucks can ship without going over their weight limit.
The first problem that I will be doing is #68 on page 539 (Dugopolski, 2012). Below, the graph shows the maximum number of TVs the 18-wheeler can hold without refrigerators, and the maximum number of refrigerators the 18-wheeler can hold without TVs.
On the X-axis, the graph shows the refrigerators, and on the Y-axis, the graph shows the TVs that the 18-wheeler can carry at a time. To find the slope of the line, I will use the two points that are on the graph, (0,330) and (110,0).
The slope is m= y1 - y2 = 0 – 330 = -330 = -3, so the slope is -3. x1 – x2 110 – 0 110
To make it easier to find how many refrigerators and how many TVs can fit in the 18-wheeler, it would be best to have a linear equation. To find the linear equation, the point-slope form can be used. y - y1 = m(x – x1) This is the point-slope form. y – 330 = -3 (x - 0) The slope is substituted for m and (330,0) is substituted for x and y. y = -3x + 330 Distributive property is used and 330 is added to both sides. y+3x ≤ 330 3x is added to both sides and the less than or equal to symbol has been changed.
The graph shown above has a solid line instead of a dotted line because the points that are on the line are a part of the solution set. Anytime the inequality symbol has the “equal to” bar, the line will be solid rather than dotted.
There are two more parts to problem #68 on page 539.
1. Will the truck hold 71 refrigerators