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Standard Form And Point Slope Form
First, Some Important slides from last time! Take Some Notes!
Review: Slope-Intercept Form
y mx b Slope Y-int.
riseslope m
run = Change in y =
= Change in x =
y
x
Slope describes a lines its steepness, incline, decline or grade.
calculate Slope With 2 Points
we have a point (x1, y1) and another point (x2, y2)
(x1, y1)
(x2, y2)
Change in y (rise) over the Change in x (run).
It looks likes this.
2 1
2 1
( )
( )
y y
x x
Review: Calculating Slope
y
x
=
Review: Finding x-int, and y-int
• Remember, to find x-int, plug in 0 for y and Solve.
• To find y-int, plug in 0 for x.
• Horizontal Lines Have no x intercept, 0 slope and equal the y-intercept!
• Vertical Lines have no y intercept, an undefined slope and equal the x intercept!
Other forms of A Line
• Just Like there are other forms of to represent fractions, there are different ways to represent a line.
• Example:
• What are some other instances when you see things in other forms?
1 31 1.52 2
Standard Form
• Another way to write the equation of a line is using Standard Form.
• A,B and C are real numbers and A and B can not be zero.
Ax By C
Slope-Int Form to Standard Form
• Suppose we wanted to see the equation of a line in standard form from slope-int form.
• Here is what we do: • Example #1
3 4y x 3 3x x
3 4x y Seriously? That’s it! Dude! Piece of Cake!
A = -3B = 1C = 4
Slope-Int Form to Standard Form
• Example #21
156
y x 1 1
6 6x x
115
6x y
Seriously? That’s it! Hot Dog! Piece of Cake!
A = -1/6B = 1C = -15
Standard Form to Slope-Int Form
• Example #3
8x + 4y = 16-8x -8x
4y = -8x + 16 Are we finished???NO!
/4 /4 /4
y = -2x + 4
Cereal? That’s it! Hot Dog! Easy as Pie!
Standard form (x- and y-int)
• How to find x and y int? Just plug in zero for x or y!
• Example #48x + 4y = 16
8(0) + 4y = 164y = 16
/4 /4
y = 4
8x + 4(0) = 168x = 16/8 /8
x = 2
Find y-int, plug in zero for x! Find x-int, plug in zero for y!
Wowsers!
Point-Slope Form
• The last form we will look at is Point-Slope Form. The hole point (Get it) of this form is an easy way to write an equation for a line using the slope, and a point (Hence the name!).
• The Form is….. • Drum Roll Tap those fingers on your desk!
1 1( )y y m x x
Point-Slope Form• Let us see how we make an equation using
Point-Slope Form.• Given that Slope equals 3 and a point (2,4),
write an equation of a line using point-slope form.
• What do we do?• We have m and x1,y1.. so..• Plug and Chug!
1 1( )y y m x x
1 13( )y y x x 1 1( )y y m x x
4 3( 2)y x
An you leave it!
One mo Time…• Slope equals -6 and a point (-2,-4), write an
equation of a line using point-slope form.• Plug and Chug!
1 16( )y y x x 1 1( )y y m x x
( 4) 6( ( 2))y x
No Way, Really? That is Simple!
4 6( 2)y x
1 1( )y y m x x
Point Slope Form to Standard and Slope-int
• We gotta do it, so lets try it out for this equation.
• First standard Form20 7( 10)y x
7 90y x
20 7 70y x -20 -20
-7x -7x
7 90x y
Time out!
It’s Slope-int!
It’s Standard!
Wow we WOW WOW!
Let’s keep on truckin’
Last Example using 2 points!
• Using (3,-6) and (-5,2), find the equation of the line using point-slope form.
• We need to find m Wait a minute, We’ve Done This!!
2 1
2 1
( ) ( 5 ( 6)) ( 5 6)
( ) (2 3) (2 3)
y ym
x x
( 5 6) 11
(2 3) 1
Last Example using 2 points!• Using (3,-6) and (-5,2), find the equation of the
line using point-slope form.• m = -1• So lets plug and chug, but which points? • They both work!!!
1 1( )y y m x x
( 6) 1( 3)y x 1 1( )y y m x x
(3,-6) (-5,2)
6 1( 3)y x
( 5) 1( 2)y x
5 1( 2)y x They Look Different, But They describe the same Line.
Don’t Believe me? Find the x and y-int!!