# 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.