Properties of Real Numbers
Name the five properties of real numbers
Associative, Commutative, Distributive, Identity, Inverse
What is slope-intercept form?
y = mx + b
How many solutions can a system of equations have? What are they?
0, 1, or infinite
What is the correct order of operations for solving equations?
Parenthesis
Exponents
Multiplication/Division
Addition/Subtraction
What is the first step to take when solving 2x + 5 = 10?
Subtract 5 from both sides
Name the property shown:
a + b = b + a (addition)
a ⋅ b = b ⋅ a (multiplication)
Commutative
What does the m stand for in y = mx + b
slope
When two lines are graphed, how can you find the solution to the system of equations?
Look at the point where the lines intersect.
Solve 2 + 2 ÷ 2
3
In the equation 3x = 15, how do I get x by itself?
Divide both sides by 3.
Name the property shown below:
(a + b) + c = a + (b + c) (addition)
(ab) c = a (bc) (multiplication)
Associative
What does the b stand for in y = mx + b
y-intercept - where the line crosses the y-axis
What are the three methods that can be used to solve a system of equations?
Elimination, Substitution, and Graphing
Solve 3 x 2 + 6 x 2
18
Solve I = Prt for r. (Rearrange the formula)
r = I/Pt
Name the property shown below:
a (b + c) = a ⋅ b + a ⋅ c
Distributive
In the point-slope form example, what is the point that lies of the line?
(y - 3) = 2(x - 4)
(3, 4)
How can you tell if the ordered pair (3, 1) is a solution to the system:
y = x + 3
x + y = 2
Plug 3 in for x and 1 in for y. If the equations are true for both, then it is a solution to the system.
Solve 3(2 + 1)
9
Solve 2x + 3 = 15 for x
What does it mean to be a closed set?
If you take two numbers from a set of real numbers and perform the operation and the answer is also in that set, then the set is closed under that operation.
In the point-slope form example, what is the slope of the line?
(y - 3) = 2(x - 4)
2
Is the graph of a circle a function? Why or why not?
No, it does not pass the vertical line test. The vertical line would touch the graph at more than one point.
Solve 2 + 4(3+1) - 2
16
Solve 2x + 4 = x + 6
x = 2