Rate of Change and Slope
Name the x-and y-intercepts for the following: 2x + 4y = 16
x-intercept: 8
y-intercept: 4
Give the correct form for a direct variation.
y = kx
A ______ ________ is an equation of a line.
Linear equation
Find the next 3 terms:
15, 9, 3, (- 3), ...
(- 9), (- 15), (- 21)
Write an algebraic expression for:
a number less thirty-five
n - 35
If "x" = 2 4 6 and
"y" = 78 156 234
Find the rate of change in simplest form
Rate of change is: 39
In the equation: y = - 6x
what is the constant of variation?
k = (- 6) ...must use "k"
What is "standard form" of a linear equation?
Ax + By = C
The 3 dots at the end of the sequence is called a what?
Ellipsis
Evaluate: 2 6
64
Find the slope for:
(- 2, 0) and (1, 5)
m = 5/3 ...need the "m"!!!
True/False
The constant of variation and slope are the same thing.
True
Values of "x" for which: f (x) = 0 are called _____ of the function "f".
Zeros
What is the formula for an arithmetic sequence?
a n = a 1 + (n - 1) d
Evaluate:
5 (14 - 5) + 6 (3 + 7)
105
Find the slope for:
(- 3, - 1) and (2, - 1)
m = 0
Suppose "y" varies directly as "x", and y = 72 when x = 8
Write a direct variation equation that relates "x" and "y"
y = kx
72 = k (8)
k = 9 therefore y = 9x
The slope of the line: y = 5 is what?
Zero
Consider the arithmetic sequence:
3, (- 10), (- 23), (- 36), ...
Write an equation for the n th term
a n = a 1 + (n - 1) d
a n = 3 + (n - 1) (- 13)
a n = - 13n + 16
Solve:
9 + 2/3x = 81
x = 108
***must have the "x" :)
Find the slope for:
(- 3, 7) and (- 3, 4)
m is undefined
Use direct variation:
If y = 3.2 when x = 1.6 find "y" when x = 19
y = kx then 3.2 = 1.6k so k = 2
y = 2x
So y = 2x or 2 (19) or 38
The graph of any direct variation equation passes through the ______ .
Origin
Consider the arithmetic sequence:
(- 12), (- 8), (- 4), 0, ...
Which term of the sequence is: 32 ?
a n = a 1 + (n - 1) d
a n = (- 12) + (n - 1) 4
a n = 4n - 16
32 = 4n - 16 so n = 12
Solve for "p"...simplest form
6p - 8n = 12
p = 4/3n + 2