Download Practice Exam 2

Practice Exam 2
You are allowed to use a 3” x 5” note card (one side) and a scientific calculator.
____________________________________________________________________________
1.
Determine whether the ordered pair (−2, 1
2.
Find at least 5 solutions of the equation, then graph the equation in the coordinate
system.
3
) is a solution of the equation 2 x + 3 = 3 y
1
y = − x−3
2
y
x
y=
(x,y)
x
3.
Identify the slope and y-intercept in the following equations and then graph the lines in
the coordinate system below, using that information. (Remember to write the y-intercepts
as points).
(a)
y = 5x − 2
y
slope:
y-intercept:
(b)
y = −2
x
slope:
y-intercept:
(c) 2y + 3x = -10
slope:
y-intercept:
4.
Without graphing the equation, find the x-intercept and the y-intercept of the equation
(6 pts)
below. (Remember to write the intercepts as points.)
3y – 2 = 5x
x-intercept:
y-intercept:
5.
Write the equation, in slope-intercept form, of the line that has a slope of 6 and passes
through the point (2, -4)
6.
A salesperson receives a fixed salary plus a specific dollar amount per item that he sells.
Suppose he receives a salary of $1350 when he sells 10 items, and $2100 when he sells
25. We can look at this information as two ordered pairs: (10, 1350) and (25, 2100).
(a)
Find the slope of the line that goes through the ordered pairs
(10, 1350) and (25, 2100)
(b)
What does the slope represent in this situation?
(c)
Find the equation of the line that represents the salesperson’s salary, y, in terms
of number of items sold x.
(d)
Find the y-intercept and explain what it represents in this situation?
7.
Determine if the following statements are true or false:
(a) The point (-5, 4) is located in quadrant III
___________
(b) The point (0, 0) is also called the origin
___________
(c) The y-coordinate is always zero for an x-intercept
___________
(d) Parallel lines have the same slope
___________
(e) Vertical lines have an undefined slope
___________
(f) 2 x + 5 y = 0 is a linear equation
___________
y
8.
Find the equations for the following lines.
(a)
x
y
(b)
x
9.
10.
Without graphing or solving the systems, determine whether the systems has no solution,
one solution, or an infinite number of solutions. Explain your answers.
(a)
y = x +2
y = -x +2
(b)
y = 2x - 3
y = 2x +3
Solve the system by the substitution method.
5x + 3y = 13
x – 2y = 0
11.
Solve the system by the addition method.
5x +3y = 12
2x = 4y + 10
12.
Solve the system by method of your choice.
3x − y = 4
2x −
13.
2
y=6
3
Solve the system by the graphing method. Then check your solution.
x + 2y = 8
y
5x + 2 y = 0
x
Check:
Write a system of equations describing the given conditions. Then solve the system using
method of your choice. Don’t forget to clearly define your variables and write a full sentence
answer.
14.
The other day I went to Staples to buy some office supplies. I bought 2 pens and 3
binders, which together cost me $9.75. My friend bought 3 of the same pens and 2 of the
same binders, and it cost her $9.00. What is the cost for a single binder and the cost for a
single pen?