MTH11 - Unit 1 Individual Project: Graphing, Trends and Forecasting

1) Solve the following:
a) 2x + 3 = 8
b) -5(x+2) + 3 = 5
c) 1/4(x) + 3/2(x) = 7
d) -5x + 1 > 11

2) a) Solve 5x + 4y = 12 for y
b) When graphed, this equation would e 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 = 16.

3) The attached graph shows Bob's salary from the year 2000 to the year 2003. He was hired in the year 2000; therefore, t = 0 represents the year 2000.
a) List the coordinates of 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 2005?

4) Suppose that the width of a rectangle is 5 inches shorter than the length and that the perimeter of the rectangle is 50.
a) Set up an equation for the perimeter 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: $42 monthly fee plus $5/hour for court rental
Option 2: No monthly fee but $8.50/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:
Option 1: C=_________________
Option 2: C=_________________
b) How many hours would you have to rent the court so 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.
If you were to connect these points with a line, where would the y-intercept be located? Give the answer in (x, y) form.