Graphs & Linear Equations Y X. Graphing Horizontal & Vertical Lines Y X This line has a y value of 4...
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Transcript of Graphs & Linear Equations Y X. Graphing Horizontal & Vertical Lines Y X This line has a y value of 4...
![Page 1: Graphs & Linear Equations Y X. Graphing Horizontal & Vertical Lines Y X This line has a y value of 4 for any x-value. Its equation is y = 4 (meaning y.](https://reader036.fdocuments.us/reader036/viewer/2022062619/551517965503465e608b4f5b/html5/thumbnails/1.jpg)
Graphs & Linear Equations
Y
X
![Page 2: Graphs & Linear Equations Y X. Graphing Horizontal & Vertical Lines Y X This line has a y value of 4 for any x-value. Its equation is y = 4 (meaning y.](https://reader036.fdocuments.us/reader036/viewer/2022062619/551517965503465e608b4f5b/html5/thumbnails/2.jpg)
Graphing Horizontal & Vertical Lines
Y
X
This line has a y value of 4 for any x-value. It’s equation is
y = 4 (meaning y always equals 4)
![Page 3: Graphs & Linear Equations Y X. Graphing Horizontal & Vertical Lines Y X This line has a y value of 4 for any x-value. Its equation is y = 4 (meaning y.](https://reader036.fdocuments.us/reader036/viewer/2022062619/551517965503465e608b4f5b/html5/thumbnails/3.jpg)
Graphing Horizontal & Vertical Lines
Y
X
This line has a x value of 1 for any y-value. It’s equation is
x = 1 (meaning x always equals 1)
![Page 4: Graphs & Linear Equations Y X. Graphing Horizontal & Vertical Lines Y X This line has a y value of 4 for any x-value. Its equation is y = 4 (meaning y.](https://reader036.fdocuments.us/reader036/viewer/2022062619/551517965503465e608b4f5b/html5/thumbnails/4.jpg)
The Equation of a Vertical Line is X=Constant
Y
X
x = 1
![Page 5: Graphs & Linear Equations Y X. Graphing Horizontal & Vertical Lines Y X This line has a y value of 4 for any x-value. Its equation is y = 4 (meaning y.](https://reader036.fdocuments.us/reader036/viewer/2022062619/551517965503465e608b4f5b/html5/thumbnails/5.jpg)
The Equation of a Horizontal Line is Y=Constant
Y
X
y = 3
![Page 6: Graphs & Linear Equations Y X. Graphing Horizontal & Vertical Lines Y X This line has a y value of 4 for any x-value. Its equation is y = 4 (meaning y.](https://reader036.fdocuments.us/reader036/viewer/2022062619/551517965503465e608b4f5b/html5/thumbnails/6.jpg)
Graph the following lines
Y = -4
Y = 2
X = 5
X = -5
X = 0
Y = 0
![Page 7: Graphs & Linear Equations Y X. Graphing Horizontal & Vertical Lines Y X This line has a y value of 4 for any x-value. Its equation is y = 4 (meaning y.](https://reader036.fdocuments.us/reader036/viewer/2022062619/551517965503465e608b4f5b/html5/thumbnails/7.jpg)
Answers
Y
X
x = 5x = -5
![Page 8: Graphs & Linear Equations Y X. Graphing Horizontal & Vertical Lines Y X This line has a y value of 4 for any x-value. Its equation is y = 4 (meaning y.](https://reader036.fdocuments.us/reader036/viewer/2022062619/551517965503465e608b4f5b/html5/thumbnails/8.jpg)
Answers
Y
X
y = -4
y = 2
![Page 9: Graphs & Linear Equations Y X. Graphing Horizontal & Vertical Lines Y X This line has a y value of 4 for any x-value. Its equation is y = 4 (meaning y.](https://reader036.fdocuments.us/reader036/viewer/2022062619/551517965503465e608b4f5b/html5/thumbnails/9.jpg)
Answers
Y
X
x = 0
y = 0
![Page 10: Graphs & Linear Equations Y X. Graphing Horizontal & Vertical Lines Y X This line has a y value of 4 for any x-value. Its equation is y = 4 (meaning y.](https://reader036.fdocuments.us/reader036/viewer/2022062619/551517965503465e608b4f5b/html5/thumbnails/10.jpg)
SLOPE =
Slope is a measure of STEEPNESS
RISE
RUN
![Page 11: Graphs & Linear Equations Y X. Graphing Horizontal & Vertical Lines Y X This line has a y value of 4 for any x-value. Its equation is y = 4 (meaning y.](https://reader036.fdocuments.us/reader036/viewer/2022062619/551517965503465e608b4f5b/html5/thumbnails/11.jpg)
The Symbol forSLOPE = m
Think of m for Mountain
![Page 12: Graphs & Linear Equations Y X. Graphing Horizontal & Vertical Lines Y X This line has a y value of 4 for any x-value. Its equation is y = 4 (meaning y.](https://reader036.fdocuments.us/reader036/viewer/2022062619/551517965503465e608b4f5b/html5/thumbnails/12.jpg)
SLOPE =
RISE
RUN
RUN
RISE•
•
How much does this line rise?
How much does it run?
(3,2)
(6,4)
(0,0) 1 2 3
1
2
4
3
5 6
4
![Page 13: Graphs & Linear Equations Y X. Graphing Horizontal & Vertical Lines Y X This line has a y value of 4 for any x-value. Its equation is y = 4 (meaning y.](https://reader036.fdocuments.us/reader036/viewer/2022062619/551517965503465e608b4f5b/html5/thumbnails/13.jpg)
SLOPE =
RISE
RUN
•
•
How much does this line rise?
How much does it run?
(3,2)
(6,4)
(0,0) 1 2 3
1
2
4
3
5 6
4
RUN 3
RISE 2
![Page 14: Graphs & Linear Equations Y X. Graphing Horizontal & Vertical Lines Y X This line has a y value of 4 for any x-value. Its equation is y = 4 (meaning y.](https://reader036.fdocuments.us/reader036/viewer/2022062619/551517965503465e608b4f5b/html5/thumbnails/14.jpg)
m=SLOPE =
•
•
(3,2)
(6,4)
(0,0) 1 2 3
1
2
4
3
5 6
4
RUN 3
RISE 2
Slopemy2 y1
x2 x1
4 2
6 3
2
3
RISE
RUNy2 y1
x2 x1
x1y1
x2y2
![Page 15: Graphs & Linear Equations Y X. Graphing Horizontal & Vertical Lines Y X This line has a y value of 4 for any x-value. Its equation is y = 4 (meaning y.](https://reader036.fdocuments.us/reader036/viewer/2022062619/551517965503465e608b4f5b/html5/thumbnails/15.jpg)
•
•
(x2,y2)(6’4)
(x1,y1)(3,2)
Switch points and calculate slopeMake (3,2) (x2,y2) & (6,4) (x1,y1)
•
•
(x1,y1)(6,4)
(x2,y2)(3,2)
![Page 16: Graphs & Linear Equations Y X. Graphing Horizontal & Vertical Lines Y X This line has a y value of 4 for any x-value. Its equation is y = 4 (meaning y.](https://reader036.fdocuments.us/reader036/viewer/2022062619/551517965503465e608b4f5b/html5/thumbnails/16.jpg)
Recalculation with points switched
Slopemy2 y1
x2 x1
4 6
2 5
2
3
2
3
•
•
(x1,y1)(6,4)
(x2,y2)(3,2)
Same slope as before
![Page 17: Graphs & Linear Equations Y X. Graphing Horizontal & Vertical Lines Y X This line has a y value of 4 for any x-value. Its equation is y = 4 (meaning y.](https://reader036.fdocuments.us/reader036/viewer/2022062619/551517965503465e608b4f5b/html5/thumbnails/17.jpg)
It doesn’t matter what 2 points you choose on a line
the slope must come out the same
![Page 18: Graphs & Linear Equations Y X. Graphing Horizontal & Vertical Lines Y X This line has a y value of 4 for any x-value. Its equation is y = 4 (meaning y.](https://reader036.fdocuments.us/reader036/viewer/2022062619/551517965503465e608b4f5b/html5/thumbnails/18.jpg)
Keeping Track of Signs When Finding The Slope Between 2 Points
• Be Neat & Careful
• Use (PARENTHASES)
• Double Check Your Work as you Go
• Follow 3 Steps
![Page 19: Graphs & Linear Equations Y X. Graphing Horizontal & Vertical Lines Y X This line has a y value of 4 for any x-value. Its equation is y = 4 (meaning y.](https://reader036.fdocuments.us/reader036/viewer/2022062619/551517965503465e608b4f5b/html5/thumbnails/19.jpg)
3 Steps for finding the Slope of a line between 2 Points
(3,4)&(-2,6)
Slopey2 y1
x2 x1
6 4
2 3
1st Step: Write x1,y1,x2,y2 over numbers
2nd Step: Write Formula and Substitute x1,x2,y1,y2 values.
3rd Step: Calculate & Simplify
(3,4) & (-2,6)x1 y1 x2 y2
6 4
2 3
2
5
2
5
![Page 20: Graphs & Linear Equations Y X. Graphing Horizontal & Vertical Lines Y X This line has a y value of 4 for any x-value. Its equation is y = 4 (meaning y.](https://reader036.fdocuments.us/reader036/viewer/2022062619/551517965503465e608b4f5b/html5/thumbnails/20.jpg)
Find the Slopes of Lines containing these 2 Points
1. (1,7) & (5,2)
5. (3,6) & (5,-5)
3. (-3,-1) & (-5,-9)
6. (1,-4) & (5,9)
4. (4,-2) & (-5,4)
2. (3,5) & (-2,-8)
![Page 21: Graphs & Linear Equations Y X. Graphing Horizontal & Vertical Lines Y X This line has a y value of 4 for any x-value. Its equation is y = 4 (meaning y.](https://reader036.fdocuments.us/reader036/viewer/2022062619/551517965503465e608b4f5b/html5/thumbnails/21.jpg)
1. (1,7) & (5,2)
5. (3,6) & (5,-5)
3. (-3,-1) & (-5,-9)
6. (1,-4) & (5,9)
4. (4,-2) & (-5,4)
2. (3,5) & (-2,-8)
Slopey2 y1
x2 x1
2 7
5 1
5
4
Slopey2 y1
x2 x1
8 5
2 3
13
5
13
5
Slopey2 y1
x2 x1
9 ( 1)
5 ( 3)
8
2
4
1
Slopey2 y1
x2 x1
5 6
5 3
11
2
Slopey2 y1
x2 x1
4 ( 2)
5 4
6
9
2
3
Slopey2 y1
x2 x1
9 ( 4)
5 1
13
4
ANSWERS
![Page 22: Graphs & Linear Equations Y X. Graphing Horizontal & Vertical Lines Y X This line has a y value of 4 for any x-value. Its equation is y = 4 (meaning y.](https://reader036.fdocuments.us/reader036/viewer/2022062619/551517965503465e608b4f5b/html5/thumbnails/22.jpg)
Solve for y if (9,y) & (-6,3) & m=2/3
Slopey2 y1
x2 x1
2
3
3 y1
6 9
3 y 15
( 15)2
3
3 y1
6 9
3 y 15
( 15)
( 5)2 3 y
10 3 y
13 y
13 y
![Page 23: Graphs & Linear Equations Y X. Graphing Horizontal & Vertical Lines Y X This line has a y value of 4 for any x-value. Its equation is y = 4 (meaning y.](https://reader036.fdocuments.us/reader036/viewer/2022062619/551517965503465e608b4f5b/html5/thumbnails/23.jpg)
Review Finding the Slopes of Lines Given 2 Points
1st Step: Write x1,x2,y1,y2 over numbers
2nd Step: Write Formula and Substitute x1,x2,y1,y2 values.
3rd Step: Calculate & Simplify
NOTE:
Be Neat, Careful, and Precise and Check your work as you go..
mSlopey2 y1
x2 x1
![Page 24: Graphs & Linear Equations Y X. Graphing Horizontal & Vertical Lines Y X This line has a y value of 4 for any x-value. Its equation is y = 4 (meaning y.](https://reader036.fdocuments.us/reader036/viewer/2022062619/551517965503465e608b4f5b/html5/thumbnails/24.jpg)
SLOPE mRISE
RUN
ZERO Slope Horizontal
Positive SlopeIs Up the Hill
Negative SlopeIs Down the Hill
NO SlopeVertical Drop
![Page 25: Graphs & Linear Equations Y X. Graphing Horizontal & Vertical Lines Y X This line has a y value of 4 for any x-value. Its equation is y = 4 (meaning y.](https://reader036.fdocuments.us/reader036/viewer/2022062619/551517965503465e608b4f5b/html5/thumbnails/25.jpg)
SLOPE mRISE
RUN
ZERO Slope Horizontal
NO SlopeVertical Drop
RISE
RUN
0
any _ number0
RISE
RUNany _ number
0Undefined(NO_ Slope)
![Page 26: Graphs & Linear Equations Y X. Graphing Horizontal & Vertical Lines Y X This line has a y value of 4 for any x-value. Its equation is y = 4 (meaning y.](https://reader036.fdocuments.us/reader036/viewer/2022062619/551517965503465e608b4f5b/html5/thumbnails/26.jpg)
Parallel LinesHave the Same Slope
RUN 3
RISE 2
•
•
(0,0) 1 2 3
1
2
4
3
5 6
4
5
RUN 3
RISE 2
![Page 27: Graphs & Linear Equations Y X. Graphing Horizontal & Vertical Lines Y X This line has a y value of 4 for any x-value. Its equation is y = 4 (meaning y.](https://reader036.fdocuments.us/reader036/viewer/2022062619/551517965503465e608b4f5b/html5/thumbnails/27.jpg)
Perpendicular LinesHave Neg. Reciprocal Slopes
(0,0) 1 2 3
1
2
4
3
5 6
m1 2
3
m2 3
2
m1 m2 2
3
3
2 1