Linear Equations and Inequalities

1) Solve the following:

a) 2x + 5 = 9

Answer:

Show your work here:

b)
Answer:

Show your work here:

c)
Answer:

Show your work here:

d)
Answer:

Show your work here:
2) a) Solve for y
Answer:

Show your work here:
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?
Slope = ______
Y-intercept = _____
c) Using your answer from part a, find the corresponding value of y when x =12.
Answer:

Show your work here:
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:
Answer:

Show your work here:
c) Find the equation of this line in slope-intercept form.
Answer:
Show or explain your work here:
d) If Bob's salary trend continued, what would his salary be in the year 2008?
Answer:
Show or explain your work here:

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.
Answer:
b) Solve this equation algebraically to find the length of the rectangle. Find the width as well.
Answer: Length ______, Width ______
Show your work here:

5) A tennis club offers two payment options:
Option1: $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:
Option 1: C=_________________
Option 2: C=_________________
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.
Answer:
Show your work here: