# Mathematics: Solving Equations and Graphing

For non-integer answers, please write your answer as a fraction rather than a decimal.

To show your work, you will need to include:

- the algebra used to compute the solution to any equations.

- the formula with substituted values.

- the final calculated answer with units.

Please see attachment for a full description of the questions in a more readable format. As well, some question are accompanied by graphs and this are visible in the attachment only:

1) Solve the following:

a) 2x + 5 = 9

b) -6(x+1) + 4 = 16

c) x/ 3 +3x/4 = 13

d) -2x + 4 > 12

2) a) Solve 5x + 6y = 18 for y

b) When graphed this equation would be a line. By examining your answer to part a, what is the slope and y-intercept of this line?

c) Using your answer from part a, find the corresponding value of y when x =12.

3) The following graph shows Bob's salary from the year 2002 to the year 2005. He was hired in the year 2002; therefore t = 0 represents the year 2002.

a) List the coordinates of any two points on the graph in (x, y) form.

b) Find the slope of this line:

c) Find the equation of this line in slope-intercept form.

d) If Bob's salary trend continued, what would his salary be in the year 2008?

4) Suppose that the length of a rectangle is 3 inches longer than the width and that the perimeter of the rectangle is 78.

a) Set up an equation involving only L, the length of the rectangle.

b) Solve this equation algebraically to find the length of the rectangle. Find the width as well.

5) A tennis club offers two payment options:

Option 1: $35 monthly fee plus $4/hour for court rental

Option 2: No monthly fee but $6.50/hour for court rental.

Let x = hours per month of court rental time.

a) Write a mathematical model representing the total monthly cost, C, in terms of x for the following:

b) How many hours would you have to rent the court so that the monthly cost of option 1, is less than option 2. Set up an inequality and show your work algebraically using the information in part a.

6) Plot the following points on the given rectangular coordinate system by clicking on the given dots and dragging them.

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#### Solution Summary

The solution is comprised of detailed explanations for the described mathematical problems which concentrate on solving line equations and graphs of a straight line. A Word file has been attached and most solutions are enclosed in that file so that they are in a more readable format.