math 222 week 2
Running Header: TWO-VARIABLE
1
Running header should use a shortened version of the title if the title is long. Page number is located at right margin.
(full title; centered horizontally & vertically)
Two-Variable Inequalities
John Q. Student
MAT 222 Week 2 Assignment
Instructor’s Name
Date
Running Header: TWO-VARIABLE
2
Two-Variable Inequalities (title required on first line)
Continuing last week’s topic of functions and relationships between variables, this week’s work examines a practical application of two-variable inequalities. As the name implies, there are independent and dependent variables, as well as graphic representations of the solutions. Because of the inequality, the graphs and solutions demonstrate a range of possible answers that would work in the given situation.
This problem is similar to #68 on page 539 (Dugopolski, 2012) for purposes of demonstrating the math needed for this writing assignment. A shipping container can carry maximum of 125 sofas and no recliners, or maximum of no sofas and 275 recliners. Study the graph and write an equation to fit the line. Pretend the triangle region is shaded in and change the equation to an inequality describing this region.
The diagram is showing the sofas on the x axis and the recliners on the y axis. There are two points on the graph, (275, 0) and (0, 125), so we can compute the slope of this line.
The slope is
Running Header: TWO-VARIABLE
3
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.
Start with the point-slope form.
Substitute the slope for m and (275, 0) for the x and y.
Use distributive property and then add 275 to both sides.
Multiply both sides by 5.
Add 11x to both sides and change to less than or equal to symbol.
The graph has a solid line rather than a dotted line indicating that points on the line itself are part of the solution
1
Running header should use a shortened version of the title if the title is long. Page number is located at right margin.
(full title; centered horizontally & vertically)
Two-Variable Inequalities
John Q. Student
MAT 222 Week 2 Assignment
Instructor’s Name
Date
Running Header: TWO-VARIABLE
2
Two-Variable Inequalities (title required on first line)
Continuing last week’s topic of functions and relationships between variables, this week’s work examines a practical application of two-variable inequalities. As the name implies, there are independent and dependent variables, as well as graphic representations of the solutions. Because of the inequality, the graphs and solutions demonstrate a range of possible answers that would work in the given situation.
This problem is similar to #68 on page 539 (Dugopolski, 2012) for purposes of demonstrating the math needed for this writing assignment. A shipping container can carry maximum of 125 sofas and no recliners, or maximum of no sofas and 275 recliners. Study the graph and write an equation to fit the line. Pretend the triangle region is shaded in and change the equation to an inequality describing this region.
The diagram is showing the sofas on the x axis and the recliners on the y axis. There are two points on the graph, (275, 0) and (0, 125), so we can compute the slope of this line.
The slope is
Running Header: TWO-VARIABLE
3
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.
Start with the point-slope form.
Substitute the slope for m and (275, 0) for the x and y.
Use distributive property and then add 275 to both sides.
Multiply both sides by 5.
Add 11x to both sides and change to less than or equal to symbol.
The graph has a solid line rather than a dotted line indicating that points on the line itself are part of the solution