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Lines, graphing, and break-even point

1. Find the slope of the line 3x - y = 5.

2. Find the point of intersection of the lines 2x + y = 4 and 3x - y = 1. Graph the pair of lines.

3. A manufacturer produces items at a daily cost of $1.50 per item and sells them for $2.50 per item. The daily operational overhead is $500. What is the break-even point?

4. Suppose the sales of a company are given by

S(x) = $300x + $3,000 where x is measured in years and x = 0
corresponds to the year 2003.

Find the predicted sales in the year 2006 assuming the trend continues.

5. Write the augmented matrix of the system: x - 2y + z = 3
2x - y = 4
3y + z = 6

6. Perform the row operation R1 + (-2) R2  R1 on the matrix .

7. y = z x + y = 5.

Determine whether this system has a unique solution, no solution, or infinitely
many solutions. If a solution exists, write it down.

8. What are the dimensions of the matrices shown below?

a) b)

9. Find

10. Find

EC. a) Find the inverse of: .

b) Use it to solve the following system of equations:
- x1 - x2 - x3 = 1
4 x1 + 5x2 = - 2
x2 - 3 x3 = 3.

Solution Preview

1. First we need to write the equation in slope-intercept form:
3x-y = 5
3x=5+y
3x-5=y
y=3x-5
The slope is the coefficient of x, so slope is 3

2. 2x+y=4
3x-y=1

We need to solve these two equations. We can do this using the substitution method:
Solve one equation for y:
Y=4-2x
Substitute this value for y in the other equation
3x - (4-2x)=1
3x-4+2x=1
5x-4=1
5x=5
x=1
Substitute this value for x in the first equation
2*1+y=4
2+y=4
y=2
Check using the second equation
3*1-2=3-2=1
x=1, y=2
Graph is on Excel file

3. Cost is 500 + 1.50x
Income is 2.50x
Break-even is where ...

Solution Summary

The expert examines the lines, graphs and break-even point. Intersection of the lines are determined. This shows how to find intersections, slope, and break-even points.

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