Transcript Graphing and Writing Equations of a Line

Take 3 sheets of paper/ fold softly (no creases)
Stagger the paper so that you have 5 tabs
Stagger the 3 like this
Then take and fold down the middle
So that it staggers as such
and
Writing
Equations
of a Line
Writing Equations of Horizontal/Vertical Lines
Writing Equation Given 2 points
Point-Slope Formula (given point & slope)
Solving for “y”
Standard Form/ x & y intercepts
Slope Intercept Form
Graphing
Right side once foldable is open
y = mx + b
m = slope
b= y-intercept (starting point when graphing
2
𝑥 −3
3
2
m=3
b = -3 (0, -3)
Start here
(o, -3)
• Slope Intercept Form
𝑦=
Given graph – find equation
b=
m=
y = mx + b
y = ___x + ____
3
Right side once foldable is open to standard tab
Ex: 3x + y = 9
3x + 0 = 9
3(0) + y = 9
3x = 9
y =9
3 3
x-int (3,0)
y-int (0,9)
Can graph (3,0) use slope to graph other points
since (0,9) is not on graph
Solving for “y”
(#, 0)
(0, #)
x y
x y
Substitute:
5x – 6y = 30
x-int.
y-int.
y=0
x=0
5x – 6(0) = 30
5(0) – 6y = 30
5x = 30
-6y = 30
5 5
-6 -6
x=6
y = -5
(6, 0)
graph points
(0, -5)
Standard Form/ x & y intercepts
x & y Intercepts
Left side once foldable is open to standard tab
Standard Form
4x – 3y = 9
-4x
-4x
-3y = -4x + 9
-3 -3 -3
Step 1
Step 2
4
𝑦 = 𝑥 −3
3
5x – y = -3
-5x
-5x
-y = -5x – 3
-1 -1 -1
y = 5x + 3
Solving for “y”
EX: 4x – 3y = 9
Step 1: Add or subtract to move “x” and its
coefficient to other side
Step 2: Divide both sides by the # (coefficient)
next to the “y”
Standard Form/ x & y intercepts
Ax + By = C
*convert to y = mx + b
Right side once foldable is open to Point – Slope tab
Given a point and slope and using y = mx + b to find “b”
(2, -4)
x, y
m=3
(substitute these values into..)
y = mx + b
-4 = 3 (2) + b
-4 = 6 + b
-6 -6
-10 = b
y = 3x + ?
* must find y-intercept (b)
m= 3 b= -10
y = 3x – 10
x, y
1
−1, 2
m=6
y = mx + b
1
2
1
2
= 6 −1 + 𝑏
= −6 + 𝑏
+6 +6
6.5 = b
y = 6x + 6.5
**only need two things to write equation of a line
Slope (m) & y –intercept (b)
**Slope is always written in fraction form, y-intercept
can be fraction or decimal
Left side once foldable is open to Point – Slope tab
Point-Slope Formula
y – y1 = m(x – x1)
Write an equation of a line through point (2, -4) with a
slope of 3.
(2, -4)
x1 , y 1
m=3
**Distribute
Solving for “y”
y – y1 = m(x – x1)
y – (-4) = 3(x – 2)
y + 4 = 3x – 6
-4
-4
y = 3x – 10
x, y
1
A −1, 2
(.5)
m=6
y – y1 = m(x – x1)
y - .5 = 6(x – -1)
y - .5 = 6x + 6
+.5
+.5
y = 6x + 6.5
**Note that we get the same equations no matter
which way we go about writing in slope-intercept form
Right side once foldable is open to Writing Equation
Given 2 points
1. Find Slope
−5 −(−3)
3 −5
=
−2
=
−2
1; m = 1
2. Use point – slope formula (choose one point- does
y – y1 = m(x – x1)
not matter which one)
y – (-5) = 1(x – 3)
(3, -5)
y+5 =x–3
x 1 , y1
-y
-y
(keep “x” positive)
5=x–y–3
+3
+3
8 = x – y Standard Form
or
x–y=8
To write in slope –intercept form using point slope…
When down to
y+5=x–3
-5
-5
y=x–8
Writing Equation Given 2 points
Write an equation in Standard Form
Given (5, -3) and (3, -5)
x1 , y 1
x2 , y 2
Left side once foldable is open to Writing Equation
Given 2 points
1. Find Slope
𝑦 −𝑦
m = 𝑥2−𝑥 1 =
2
1
−3 −1
7 −5
=
−4
=
2
-2 m = -2
2. Choose one point to use to plug into pt slope
formula- (does not matter which one)
m = -2 (5,1)
y – y1 = m(x – x1)
y – 1 = -2(x – 5)
y – 1 = -2 x + 10 Distributed – 2 to ()
+1 =
+1
y = -2x + 11
OR
Use point and slope and plug into y = mx + b
m = -2
(5, 1)
x, y
y = mx + b
1 = -2(5) + b
1 = -10 + b
+10 +10
11 = b
** only need slope (m) and
y-intercept (b) to write
y = -2x + 11
equation of a line. m = -2 b = 11
Writing Equation Given 2 points
Write an equation of a line through A(5,1) and B(7,-3)
x1 , y 1
x2 , y 2
Write an equation of a horizontal line through
point (-2, 5)
Hint graph the point first
m=0
b=5
can make a “z” with
horizontal line
y=5
Write an equation of a vertical line through (-2, 5)
The line does not cross the y-axis
therefore; there is no y-int. (b)
m = undefined
x = -2
U
ndefined
Writing Equations of Horizontal/Vertical Lines
Right side once foldable is open to Writing Equation
of Horizontal/ Vertical Lines
Given a graph write the equation
**Hint (create a table)
x
y
-1
0
1
2
2
2
y does not ever change
y = mx + b
m=0 b=2
y=0x+2
y =2
x
y
4
4
4
-1
0
1
there is not y-int (b)
therefore; no y =
x=4
Writing Equations of Horizontal/Vertical Lines
Left side once foldable is open