Linear Equations
What is the slope in the equation y = 3x + 5?
slope = 3
What is the definition of a function?
A function is a relation where each input (x-value) has exactly one output (y-value).
How many degrees are in a straight angle?
A straight angle has 180°
What type of number is √16: rational or irrational?
√16 = 4, which is rational.
Simplify: 3².
: 32=∗∗9∗∗3^2 = **9**32=∗∗9∗∗
What does it mean when a line has a slope of 0?
A slope of 0 means the line is horizontal (y = constant).
Determine whether the table represents a function:
x: 1, 2, 3, 3
y: 4, 5, 6, 7
Not a function. x = 3 corresponds to two different outputs (6 and 7).
What is the Pythagorean Theorem?
Pythagorean Theorem: a² + b² = c² for a right triangle (c = hypotenuse)
Is π rational or irrational?
π is irrational.
What is the product rule for exponents?
Product rule: am⋅an=am+na^m \cdot a^n = a^{m+n}am⋅an=am+n (when bases are the same).
Write an equation of a line with slope 2 passing through (0, –4).
Equation: y = 2x − 4 (slope 2, passes through (0, −4)).
What does the “vertical line test” check for?
The vertical line test checks whether a vertical line intersects the graph more than once; if so, it's not a function.
Find the perimeter of a rectangle with length 8 and width 5.
Perimeter = 2(8+5)=262(8 + 5) = 262(8+5)=26. So 26 units.
Simplify: –3 – 7.
–3 – 7 = –10.
Simplify: x³ · x⁴.
x3⋅x4=x3+4=∗∗x7∗∗x^3 \cdot x^4 = x^{3+4} = **x^7**x3⋅x4=x3+4=∗∗x7∗∗.
Is the equation 2x – 4y = 8 linear? Why or why not?
Yes. 2x − 4y = 8 is linear because variables appear to the first power and it can be written in the form y = (1/2)x − 2.
If f(x) = 2x – 1, what is f(5)?
: f(5) = 2(5) − 1 = 9.
Two angles add up to 90°. What are they called?
They are complementary angles (two angles summing to 90°).
Place these in order from least to greatest: –5, 0, –2, 4.
Least to greatest: –5, –2, 0, 4
Simplify the polynomial: (3x + 2) + (5x – 7).
(3x+2)+(5x−7)=∗∗8x−5∗∗.
A line passes through (–2, 1) and (4, 7). What is the slope?
Slope between (−2, 1) and (4, 7) = (7−1)/(4−(−2))=6/6=∗∗1∗∗(7−1)/(4−(−2)) = 6/6 = **1**(7−1)/(4−(−2))=6/6=∗∗1∗∗
Describe how the graph of y = x + 3 is different from y = x.
y = x + 3 is the graph of y = x shifted up 3 units (y-intercept 3 instead of 0).
A right triangle has legs of length 9 and 12. What is the hypotenuse?
Hypotenuse = 92+122=81+144=225=∗∗15∗∗\sqrt{9^2 + 12^2} = \sqrt{81 + 144} = \sqrt{225} = **15**92+122=81+144=225=∗∗15∗∗.
What is the absolute value of –12, and what does absolute value represent?
Absolute value of –12 is 12. Absolute value represents distance from 0 on the number line.
Expand: (x – 4)(x + 2).
(x−4)(x+2)=x2−2x−8(x − 4)(x + 2) = x^2 − 2x − 8(x−4)(x+2)=x2−2x−8.