Point-Slope Form Linear Equations in Two Variables.
-
Upload
agnes-welch -
Category
Documents
-
view
223 -
download
1
Transcript of Point-Slope Form Linear Equations in Two Variables.
![Page 1: Point-Slope Form Linear Equations in Two Variables.](https://reader030.fdocuments.us/reader030/viewer/2022032703/56649d0e5503460f949e4045/html5/thumbnails/1.jpg)
Point-Slope Point-Slope FormFormLinear Equations in
Two Variables
![Page 2: Point-Slope Form Linear Equations in Two Variables.](https://reader030.fdocuments.us/reader030/viewer/2022032703/56649d0e5503460f949e4045/html5/thumbnails/2.jpg)
What we Know so far….What we Know so far….
Slope Intercept Form
bmxy
Where m is the slope and b is the intercept
![Page 3: Point-Slope Form Linear Equations in Two Variables.](https://reader030.fdocuments.us/reader030/viewer/2022032703/56649d0e5503460f949e4045/html5/thumbnails/3.jpg)
What is Slope?What is Slope?
- SLOPE -
- SLOPE - +SL
OPE
+
+SLOPE
+
Steep
ness
RiseRun
Change in Y
Change in XAmount of Slanty=mx + b
![Page 4: Point-Slope Form Linear Equations in Two Variables.](https://reader030.fdocuments.us/reader030/viewer/2022032703/56649d0e5503460f949e4045/html5/thumbnails/4.jpg)
Slope Summary
Slope = 0Positi
ve Slope
Negative Slope
Down the
slopes Undefined Slope
Cross country skiingUp the ski lif
t
Oops!
![Page 5: Point-Slope Form Linear Equations in Two Variables.](https://reader030.fdocuments.us/reader030/viewer/2022032703/56649d0e5503460f949e4045/html5/thumbnails/5.jpg)
5
y
x
2-2
The slope of a line is a number, m, which measures its steepness.
m = 0
m = 2m is undefined
m =1
2
m = -1
4
![Page 6: Point-Slope Form Linear Equations in Two Variables.](https://reader030.fdocuments.us/reader030/viewer/2022032703/56649d0e5503460f949e4045/html5/thumbnails/6.jpg)
The New Stuff… Point- Slope The New Stuff… Point- Slope FormFormPoint- Slope form is:
)( 11 xxmyy Where m is the slope
and (x1, y1) is the given point
![Page 7: Point-Slope Form Linear Equations in Two Variables.](https://reader030.fdocuments.us/reader030/viewer/2022032703/56649d0e5503460f949e4045/html5/thumbnails/7.jpg)
Write the Equation in Point-Slope Write the Equation in Point-Slope FormForm
)6,1(3
1 andm
)( 11 xxmyy Step 1: Plug it in
Point- Slope Form
Slope – Intercept Form
![Page 8: Point-Slope Form Linear Equations in Two Variables.](https://reader030.fdocuments.us/reader030/viewer/2022032703/56649d0e5503460f949e4045/html5/thumbnails/8.jpg)
8
A linear equation written in the form
y – y1 = m(x – x1) is in point-slope form.
The graph of this equation is a line with slope m passing through the point (x1, y1).
Example:
The graph of the equation
y – 3 = - (x – 4) is a line
of slope m = - passing
through the point (4, 3).
1
2 1
2
(4, 3)
m = -1
2
x
y
4
4
8
8
Plot the point, then rise & run from there….
![Page 9: Point-Slope Form Linear Equations in Two Variables.](https://reader030.fdocuments.us/reader030/viewer/2022032703/56649d0e5503460f949e4045/html5/thumbnails/9.jpg)
Using Point-Slope FormUsing Point-Slope Form
1 2 43
5
-1-2-3-4-5
1234
5-1-2-3-4-5
(2,2)
We need the slope and a point: )2,2(2
5andm
Plug them into the point-slope form
)( 11 xxmyy
)2(2
52 xy
Point – Slope Form
![Page 10: Point-Slope Form Linear Equations in Two Variables.](https://reader030.fdocuments.us/reader030/viewer/2022032703/56649d0e5503460f949e4045/html5/thumbnails/10.jpg)
10
Example: Write the point-slope form for the equation of the line through the point (-2, 5) with a slope of 3.
Use the point-slope form, y – y1 = m(x – x1), with m = 3 and (x1, y1) = (-2, 5).
y – y1 = m(x – x1)
y – 5 = 3(x – (-2)) Let m = 3, let (x1, y1) = (-2, 5).
y – 5 = 3(x + 2) Simplify into point-slope form
![Page 11: Point-Slope Form Linear Equations in Two Variables.](https://reader030.fdocuments.us/reader030/viewer/2022032703/56649d0e5503460f949e4045/html5/thumbnails/11.jpg)
Given two points, write the equation of a line in point-slope form
Steps:
1. Find slope 2. Place a point and the slope in into point
slope form
3. Point-Slope form
(2,-3) and (4,-2)
2 3
4 2
2 3
2
1
2
y y1 m(x x1)
y 3 1
2(x 2)
y 3 1
2(x 2)
)2(2
13 xy
42
1 xy
Slope-intercept form
Solve for y & get ..
![Page 12: Point-Slope Form Linear Equations in Two Variables.](https://reader030.fdocuments.us/reader030/viewer/2022032703/56649d0e5503460f949e4045/html5/thumbnails/12.jpg)
Simplify using distributive property, then move the constant to the right side & combine like terms
52
52 xy
)2(2
52 xy
32
5 xy
Or move the constant to the right side, then distribute & combine like terms
To write point-slope into slope-intercept:
)2(2
52 xy
2)2(2
5 xy
252
5 xy
32
5 xy
252
5 xy
![Page 13: Point-Slope Form Linear Equations in Two Variables.](https://reader030.fdocuments.us/reader030/viewer/2022032703/56649d0e5503460f949e4045/html5/thumbnails/13.jpg)
13
Example: Write the slope-intercept form for the equation of the line through the points (4, 3) and (-2, 5).
y – y1 = m(x – x1) Point-slope form
Slope-intercept formy = - x + 13
31
3
2 1 5 – 3 -2 – 4
= - 6
= - 3
Calculate the slope.m =
Use m = - and the point (4, 3).y – 3 = - (x – 4)1
3 3
1
Solve for y…
![Page 14: Point-Slope Form Linear Equations in Two Variables.](https://reader030.fdocuments.us/reader030/viewer/2022032703/56649d0e5503460f949e4045/html5/thumbnails/14.jpg)
A ChallengeA Challenge
Can you write the equation of a line in point-slope form that passes through (-3,6) and (1,-2)
8 2 6 + 2 -3 – 1
= - 4
= - 1
Calculate the slope.m =
y – y1 = m(x – x1)
y + 2 = - 2 (x – 1)
Use m = - 2 and the point (1, -2).
y = -2(x – 1) - 2
y = -2x + 2 - 2
y = -2x + 0 y = -2x
Point-Slope Form
Slope-Intercept Form
![Page 15: Point-Slope Form Linear Equations in Two Variables.](https://reader030.fdocuments.us/reader030/viewer/2022032703/56649d0e5503460f949e4045/html5/thumbnails/15.jpg)
Applications
1. Raymond ordered rose bushes for his back yard. They cost $15 each. The shipping cost was $10. If his bill was $85, how many rose bushes did he order?– What are the variables (what letters will you
use)?– Write the equation using the variables.– Solve the equation and answer the question
![Page 16: Point-Slope Form Linear Equations in Two Variables.](https://reader030.fdocuments.us/reader030/viewer/2022032703/56649d0e5503460f949e4045/html5/thumbnails/16.jpg)
1. Raymond ordered rose bushes for his back yard. They cost $15 each. The shipping cost was $10. If his bill was $85, how many rose bushes did he order?
– VARIABLES: r (rose bushes) and s (shipping)– EQUATION: 15 r + s = 85– SOLVE: 15 r + 10 = 85
15 r = 75 r = 5
Raymond ordered 5 rose bushes
![Page 17: Point-Slope Form Linear Equations in Two Variables.](https://reader030.fdocuments.us/reader030/viewer/2022032703/56649d0e5503460f949e4045/html5/thumbnails/17.jpg)
2. The length of a rectangle is 6 inches longer than its width. The perimeter is 36 inches. What are the length and width?– What are the variables (what letters will you
use)?– Write the equation using the variables.– Solve the equation and answer the question
![Page 18: Point-Slope Form Linear Equations in Two Variables.](https://reader030.fdocuments.us/reader030/viewer/2022032703/56649d0e5503460f949e4045/html5/thumbnails/18.jpg)
2. The length of a rectangle is 6 inches longer than its width. The perimeter is 36 inches. What are the length and width?
– VARIABLES: L (length) and W (width)– EQUATION: L + W + L + W = 36
and L = 6+W– SOLVE: (6+W) + W + (6+W) + W = 36
12 + 4W = 36 4W = 24 W = 6
The length is 12 and the width is 6