Transcript 幻灯片 1 - TangHua2012-2013

Chapter 6: Linear Function
Group Member: Angela, Vincent, Krystal, Antony
Agenda
 What is slope? What is the formula to calculate slope?
How to determine slope through two points on a line?
 How to verify a parallel line or a perpendicular line to a
given one?
 How to calculate a parallel or a perpendicular line to a
given one?
 How to use slope to identify polygon?
 Three different forms of writing an equation of a linear
function.
 Using an Equation of a Linear Function to Solve a
Problem.
Slope
 Slope is the steepness of a roof is measured by calculating
its slope.
 The formula of the slope is: Slope= Rise/Run
Hint:
Rise: The vertical distance from the bottom of edge of the roof to
the top
Run: The corresponding horizontal distance.
Example
 Calculate the slope of
the linear function.
From the graph, we can see
that the rise=2, the run=1.
Then we can calculate the
slope:
Slope=Rise/Run
=2/1
=1
Parallel Lines
 If two lines have the same slope, the two lines parallel
to each other.
 Example:
 y=2x+1 and y=2x+3
Perpendicular Lines
 If two line perpendicular to each other, that means that
the two slopes are negatively reciprocal to each other.
 Example: y=2x+1 and y=-1/2 x+1
How to determine a parallel line to a given one?
 In this graph, the linear function of this line is y=2x+1.
Can you write a linear function that is parallel to the line?
Solution




The parallel line and the given line should have the same slope.
The slope of the given line is : 2
So, the slope of the line should be: 2
So, the linear function of the line should be y=2x+2/3/4, etc.
How to determine a perpendicular line to a given one?
 In this graph, the linear function of this line is y=2x+1. Can
you write a linear function that is perpendicular to the line?
Solution
 The perpendicular line’s slope the negative reciprocal of the slope of the
given line.
 The slope of the given line is : 2
 So, the slope of the line should be: -1/2
 So, the linear function of the line should be y=-1/2x + 1/2/3/4, etc.
How to use slope to identify polygon?
 ABCD is a parallelogram. Is it a rectangle? Justify the answer.
d
a
c
b
Solution
 ABCD is a parallelogram. If one of the angle is 90, we can prove that it is a
rectangular.
 Step 1: we can determine the slope of line AB and line AD
 Step 2: we can identify whether the slope of AB is the negative reciprocal
of slope AD.
 Step 3:we can easily identify whether it is a rectangle or not.
Slope-Intercept Form
 y-intercept form: y=2x+1
Advantage: We can easily determine the intersection with y-axis
Slope-Point Form
 Slope-point form: y-y1=m(x1-x2)
 Example: y-2=1/3*(x+4)
Advantage: We can easily know that (-4,2) is
on this line.
General Form
 General form can be represented as: ax+by+c=0
 Example: 2x+3y-12=0
Hint: You should always check the order-----x
y
number