February 17 2015
Transcript of February 17 2015
Warm - Up; Khan Topic Continue Slope Practice
Slope - Intercept Formula
Interpreting Graphs of Linear
and Non-Linear Functions
Khan Academy
Khan Academy
nonlinear
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Linear/ Nonlinear
Given this,
what are the x and y axes?
faster 1
67twice
• Find the range of the function below when the domain is {-4, -1, 3} y = |x| - 2
Warm Up/Test Review
4 0 0 -13
The Slope of a Li
ne
x
y
x2 – x1
y2 – y1
change
in ychange in x
The slope of the line passing through the two points (x1, y1) and (x2, y2) is given by the formula
(x1, y1)
(x2, y2)
y2 – y1
x2 – x1
m = , (x1 ≠ x2 ).
The rise is the difference of the y-values of two points on a line.The run is the difference in the x-values of two points on a line.
The constant rate of change of a straight line is called the slope.
The Slope of a Line:
Slope is usually represented by the letter m (from the French, monter, which
means “to go up”).
Straight Lines (linear functions) are straight because the slope never changes!!
(3, 2)
(–1, –2)
Then count horizontally to a second point to find the run.
Count vertically from any one point on the line to find the rise.
Finding the Slope of a Line
slope = = 1
The slope of the line is 1.
It does not matter which ordered pair you start with.
slope = = 1
44
(5, 4)
Then count horizontally to a second point to find the run.
Count vertically from any one point on the line to find
the rise.
slope = =
The slope of the line is
slope = =
Find the slope of the line:
It does not matter which y you begin from.
(1, 2)
The Slope of a Line
The slope of a line is the ratio of rise to run for any two points on the line.change in y
change in x Rise Run=
Find the slope of the line passing through the points (2, 3) & (4, 5).
The x1 and y1 must come from the same ordered pair.
y2 – y1
x2 – x1
m = 5 – 3 4 – 2
= = 22
= 1
2
2(2, 3)
(4, 5)
x
y
The Slope of a Line
Name one other ordered pair on this
line.
The Slope of a LineWhat is the slope of this, and all horizontal lines?Don't guess,
just plug the numbers in...
All horizontal lines have a slope of zero.
The Slope of a LineWhat is the slope of this, and all vertical lines?
All vertical lines have a slope that is undefined because... a
denominator cannot be zero.
y
x2-2
The slope of a line is a number, m, which measures its steepness.
m = 0
m = 2
m is undefined
m =12
m = - 14
The slope of a line reveals how the f(x) is affected by a change in x
What does a steeper line tell you about the y
variable?
y2 – y1
x2 – x1m =
The Slope of a Line
The Slope of a Line
What is the slope of the line?
The Slope of a Line
Find the next point in both directions
Find the slope of each line:
23
m =
m = m = -
1
Grand Prix Go-Carts:
What is the y-intercept?
What are the independent (x) and dependent (y)
variables?How does each change in the x variable affect the dependent, y variable? In other words, what is the rate of change?Which graph shows the price function?
Test Review:
A
BC
D E
Is this graph a function?By what percent did the price of silver
drop between Aug. 7th & August 9th?36%
Test Review: