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First let’s review 5.1. Write the equation in slope-intercept form, given m = 3 ang b = (0,-2). Example m = 3, b = (0,-2). y = mx + b. y = __ x + ___. Write the equation of the line in slope-intercept form. m = 3/2. b = (0,1). y = mx + b. - PowerPoint PPT Presentation
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First let’s review 5.1
Write the equation in slope-intercept form, given m = 3 ang b = (0,-2)Example
m = 3, b = (0,-2)
y = __ x + ___
€
y = 3x − 2y = mx + b
Write the equation of the line in slope-intercept form.
m = 3/2
b = (0,1)
€
y =3
2x +1
y = mx + b
Given this equation, what is the slope and y-intercept?
€
−2x + 3y =15
€
y =2
3x + 5
m = 2/3
b = (0,5)
+2x +2x
3y = 2x + 15
3 3 3
Review 5.2 Point-Slope Form
Write the equation of the line in point-slope form.
m = -1/3
€
y − 3 =−1
3(x − 0)
(0,3)
(3,2)
€
y − 2 =−1
3(x − 3)
Or you can use any point
1 1y y m x x
€
y − y1 = m(x − x1)
€
y − 3 = −2(x − 2)Now leave youranswer in slope-intercept form.
€
y − 3 = −2x + 4
+3 +3
€
y = −2x + 7
This is the equation of the line in point-slope form!!
Given (2,3) and slope = -2, write the equation in SLOPE-INTERCEPT
€
y − y1 = m(x − x1)
€
y − 4 = −3
2(x + 8)
Now leave youranswer in slope-intercept form.
€
y − 4 = −3
2x −12
+4 +4
€
y = −3
2x − 8
This is the equation of the line in point-slope form!!
Given (-8,4) and slope = -3/2, write the equation in SLOPE-INTERCEPT
5.3 Writing equations of a line given two points
Forms of a linear equation
Slope-intercept Form y = mx + b
Point-Slope Form y – y1 = m(x – x
1)
If given two points,
First, find the slope using the slope formula.
Example
contains (5, –8) and (2, 7)
2 1
2 1
y ym
x x
m = 7 – -8 2 – 5
m = 15 –3
m = –5
(x1 , y1) and (x2 , y2)
If given two points,
Then use the slope and EITHER point to worklike the previous example.
y – y1 = m(x – x
1)
y – 7 = – 5(x – 2)
y – 7 = –5x + 10
y = –5x + 17
m = –5, contains (5, –8) and (2, 7)
Writing an Equation Given Two Points
1. Calculate the slope of the line.
2. Select the form of the equation.
a. Slope-intercept form
b. Point-slope form
y mx b
1 1y y m x x
3. Substitute and/or solve for the selected form.
Writing an Equation Given Two Points
1,3 5, 2
3 2
1 5m
5
4
5
4
2 3
5 1m
5
4
5
4
or
Given the two ordered pairs, write the equation of the line in point-slope form.
Calculate the slope.
Writing an Equation Given Two Points in point-slope form:
1,3 5, 25
4m
1 1y y m x x
53 1
4y x 5
2 54
y x
Point-slope form
Same example: Writing an Equation Given Two Points in slope-intercept form.
1,3 5, 25
4m
53 1
4y x 5
2 54
y x
5 53
4 4y x
5 53 3 3
4 4y x
5 17
4 4y x
5 252
4 4y x
5 252 2 2
4 4y x
5 17
4 4y x
Start by using point-slope form:
2.) Writing an Equation Given Two Points in slope-intercept form.
(-5,7) (2,-7)
€
m =−7 − 7
2 − −5=
−14
7= −2
Start by using point-slope form:
€
y − y1 = m(x − x1)
€
y − 7 = −2(x + 5)
€
y + 7 = −2(x − 2)
€
y − 7 = −2x −10
€
y + 7 = −2x + 4+ 7 + 7 - 7 - 7
€
y = −2x − 3
€
y = −2x − 3
EVERY ONE GET A COMMUNICATOR:
WITH A BLANK SIDE!!
3.) Writing an Equation Given Two Points in slope-intercept form.
€
m =6 − 0
−2 − 2=
6
−4=
−3
2Start by using point-slope form:
€
y − y1 = m(x − x1)
€
y − 0 =−3
2(x − 2)
€
y − 6 =−3
2(x + 2)
€
y =−3
2x + 3
€
y − 6 =−3
2x − 3
+ 3 + 3
€
y =−3
2x + 3
(2,0) (-2,6)
4.) Writing an Equation Given Two Points in slope-intercept form.
€
m =4 − −5
8 −10=
9
−2=
−9
2Start by using point-slope form:
€
y − y1 = m(x − x1)
€
y + 5 =−9
2(x −10)
€
y − 4 =−9
2(x − 8)
€
y + 5 =−9
2x + 45
€
y + 7 =−9
2x + 36
- 5 - 5
- 7 - 7
€
y =−9
2x + 40
€
y =−9
2x + 29
(10,-5) (8,4)
5.) Writing an Equation Given Two Points in slope-intercept form.
€
m =5 − 5
−3 − 6=
0
−9= 0
Start by using point-slope form:
€
y − y1 = m(x − x1)
€
y − 5 = 0(x − 6)
€
y − 5 = 0(x + 3)
€
y − 5 = 0
€
y − 5 = 0+ 5 + 5 + 5 + 5
€
y = 5
€
y = 5
(6,5) (-3,5)
Horizontal line
6.) Writing an Equation Given Two Points in slope-intercept form.
€
m =8 − −4
−4 − −2=
12
−2= −6
Start by using point-slope form:
€
y − y1 = m(x − x1)
€
y − 7 = −2(x + 5)
€
y + 7 = −2(x − 2)
€
y − 7 = −2x −10
€
y + 7 = −2x + 4+ 7 + 7 - 7 - 7
€
y = −2x − 3
€
y = −2x − 3
(-2,-4) (-4,8)
7.) Writing an Equation Given Two Points in slope-intercept form.
€
m =1 − 6
9 − −6=
−5
15=
−1
3Start by using point-slope form:
€
y − y1 = m(x − x1)
€
y − 7 = −2(x + 5)
€
y + 7 = −2(x − 2)
€
y − 7 = −2x −10
€
y + 7 = −2x + 4+ 7 + 7 - 7 - 7
€
y = −2x − 3
€
y = −2x − 3
(-6,6) (9,1)
NOW WHAT IF I GAVE YOU A GRAPH, TELL ME THE EQUATION OF THE LINE:
WHAT’S THE MAJOR DIFFERENCE BETWEEN THESE TWO GRAPHS:
The one on the right does nothave a CLEAN y-intercept!!
So creating an equation using slope-intercept form would NOT work!!!
Create the equation of the line using two points on the line:
(-3,4) (5,8)
