# Topic F

Document Sample

Topic I
Slope

8.2.spi11
Finding the slope of a line:
   The slope of a hill means how steeply it goes
up or down. Lines and curves also have a
slope.
   To find slope:

   Slope = change in y
change in x
8

Slope = change in y
Graph (-4, 2)               change in x
and (1,3)
6
Slope = 1
5

4

2

-5                                        5
   The slope of a line through (-4,2) and (1,3) is
1/5.

   Go from the left point to the right point you
count 1 up and 5 across.

   Slope = change in y = 1
change in x = 5
Finding Slope of a Line
 Designate two points as : (x ,y ) and (x ,y )
 Formula for calculating the slope between
two points:
 Slope = y -y

x -x
The formula really means:
Slope = the difference of the y-coordinates
the difference of the x-coordinates
Example
   Find the slope of the line through

(-4,2) and (1,3).

 Use the slope formula:
= y -y
x -x
= 3 -2
1-(-4)

= 1/5
(3,5)
What is the          5

slope of this        4

line?                3
(2,3)

2

1
(1,1)

-6     -4     -2                    2               4   6

-1
(0,-1)

-2

(-1,-3)   -3

-4

-5
How to find slope:
   Pick any two coordinates:
   I picked (2,3) and (3,5)

   Slope = 5-3 = 2 = 2
3-2 1

** If a graph is given to you without coordinates,
then estimate what the coordinates would be.
Then just plug in your coordinates into the
slope formula. Remember that the
coordinates can be ANYWHERE on the line!!
Finding slope Using its
Equation
   Find the slope of y = 3x – 4

   Let x be zero and two. Then calculate the
corresponding y-coordinates. With those two
points, you can graph the line and calculate
the slope.
   First, make a graph with the number 0 and 2
being x.        x          y
0     3(0) – 4 = -4
2     3(2) – 4 = 2
4

   The points are     3

   (0,-4) and (2,2)
2
(2,2)

1

-4        -2                 2           4

-1

-2

-3

-4
(0,-4)
Solve for the slope:
   Now put the coordinates into the slope
formula to solve:

   (0,-4) and (2,2)

   2 – (-4) = 6 = 3
2–0       2
Short-Cut!
   A short-cut for finding slope from an equation:

   y = 3x – 4 (this was our equation)

   y = mx + b (this is the same equation without
numbers)

   The number with “x” is the slope! The other number
is just where the slope lays on the y axis.

   So the slope in the equation y = 3x – 4 is simply 3.
Horizontal lines have a slope of
zero while vertical lines have no
slope

m=
0
Vertical                   Horizontal
m=
no
slope
Slope-Intercept Form:
y = 2x + 4

Standard Form:
-2x + y = 4
Intercepts
   X-intercept – point at which the line crosses
the x-axis
   To find the x-intercept, plug in 0 for y

   Y-intercept – point at which the line crosses
the y-axis
   To find the y-intercept, plug in 0 for x
Slope intercept form is:

y = mx + b
Our main goal is to get the y
alone on one side of the
equation
Convert Into Slope-Intercept Form

2 y  4x  2
(divide both sides by 2 to get y alone)

2 y  4x  2
2        2
(now simplify all fractions)

2 y  4x  2
2               1

2    2    2
y  2x  1
When an equation is in slope-intercept
form:

Now look at the equation below……

y  2x  1
What is the slope? ____________

What is the intercept? ____________
*** Easy ***
Convert to Slope-Intercept Form:
5y = 10x + 15
(divide both sides by 5 to get y alone)
5 y  10 x  15
5        5
(now simplify all fractions)
5 y  10 x  15
5       5            5

y = 2x + 3 BRAVO!!
*** Now Try this Convert to
Slope-Intercept Form ***

-3y = -9x - 12

Step 1: divide both sides by -3 to get y alone

Step 2: Simplify all fractions

Step 3: Write your equation in y = mx + b
What is the slope? ____________

What is the intercept? ____________

-3y = -9x - 12        (divide both sides by -3 to get y alone)
-3     -3
(now simplify all fractions)
-3y = -9x - 12
-3    -3 -3
y = 3x + 4
Slope = 3
Wow, you’re good
Intercept = 4        at this!!
*** Now Try this Convert to Slope-
Intercept Form ***

2y + 26 = -6x
Step 1: Subtract both sides by 26

Step 2: Divide both sides by 2 to get y by itself

Step 3: Simplify all fractions

What is the slope? ____________

What is the intercept? ____________
2y + 26 = -6x     (subtract both sides by 26)
26        -26
(now divide both sides by 2
2y = -6x - 26
2 2 2
(simplify all fractions)

y = -3x - 13

You are a math wizard!
Example

Using 4x – 2y = 12, what is the slope and the
intercepts?
   X-intercept:           Slope:
   4x – 2(0) =12          Use the intercepts to
   4x=12                   find the slope (3,0) and
   X=3                     (0,-6)
   Change in y: -6-0=-6
   Change in x: 0-3 = -3
   Y-intercept
   M= -6 = 2
   4(0) -2y=12
3
   -2y=12
   Y=-6
Write the equation of a line that
has a y-intercept of -3 and a
slope of -4.
1. y = -3x – 4

2. y = -4x – 3

3. y = -3x + 4

4. y = -4x + 3
Write an equation of the line that
goes through the points (0, 1) and
(1, 4).

1.   y = 3x + 4
2.   y = 3x + 1
3.   y = -3x + 4
4.   y = -3x + 1
Find the slope and y-intercept of
y = -2x + 4
1.   m = 2; b = 4
2.   m = 4; b = 2
3.   m = -2; b = 4
4.   m = 4; b = -2

DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
 views: 0 posted: 9/16/2012 language: simple pages: 28
How are you planning on using Docstoc?