remediation. slope find the slope of a line given two points: (3, 4) and (7, 8). m = (8 – 4)/(7...
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![Page 1: Remediation. Slope Find the slope of a line given two points: (3, 4) and (7, 8). m = (8 – 4)/(7 – 3) = 4/4 = 1 The slope is 1](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f335503460f94c4f6eb/html5/thumbnails/1.jpg)
Remediation
![Page 2: Remediation. Slope Find the slope of a line given two points: (3, 4) and (7, 8). m = (8 – 4)/(7 – 3) = 4/4 = 1 The slope is 1](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f335503460f94c4f6eb/html5/thumbnails/2.jpg)
Slope
run
rise
xx
yym
12
12
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Slope
Find the slope of a line given two points: (3, 4) and (7, 8).
m = (8 – 4)/(7 – 3) = 4/4 = 1 The slope is 1.
![Page 4: Remediation. Slope Find the slope of a line given two points: (3, 4) and (7, 8). m = (8 – 4)/(7 – 3) = 4/4 = 1 The slope is 1](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f335503460f94c4f6eb/html5/thumbnails/4.jpg)
Y-intercept
The y-intercept is where the line crosses the y axis.
It is written (0, #) since the x part of the point is 0 when it goes across the y axis.
To find the y-intercept in a line, put in 0 for x and solve for y.
![Page 5: Remediation. Slope Find the slope of a line given two points: (3, 4) and (7, 8). m = (8 – 4)/(7 – 3) = 4/4 = 1 The slope is 1](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f335503460f94c4f6eb/html5/thumbnails/5.jpg)
Y-intercept
Given the line y = 2x + 5, find the y intercept.
First substitute in 0 in place of x. y = 2(0) + 5 Now solve for y y=5 This the y-intercept. (0, 5)
![Page 6: Remediation. Slope Find the slope of a line given two points: (3, 4) and (7, 8). m = (8 – 4)/(7 – 3) = 4/4 = 1 The slope is 1](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f335503460f94c4f6eb/html5/thumbnails/6.jpg)
X-intercept
The x-intercept is where the line crosses the x axis.
It is written (#, 0) since the y part of the point is 0 when it goes across the x axis.
To find the x-intercept in a line, put in 0 for y and solve for x.
![Page 7: Remediation. Slope Find the slope of a line given two points: (3, 4) and (7, 8). m = (8 – 4)/(7 – 3) = 4/4 = 1 The slope is 1](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f335503460f94c4f6eb/html5/thumbnails/7.jpg)
X-intercept
Given the line y = 2x + 5, find the x intercept.
First substitute in 0 in place of y. 0 = 2x + 5 Now solve for x -5 = 2x -5/2 = x This the x-intercept. (-5/2, 0)
![Page 8: Remediation. Slope Find the slope of a line given two points: (3, 4) and (7, 8). m = (8 – 4)/(7 – 3) = 4/4 = 1 The slope is 1](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f335503460f94c4f6eb/html5/thumbnails/8.jpg)
Assignment:Find the slope of the line that passes through the points:
1)(-5, 3) and (0, 0)
2)(-3, 7) and (5, -3)
3)(-3, 8) and (-3, -4)
4)(13.5, 6) and (-11, 6)
0.4
.34
5.2
5
3.1
m
undefinedism
Click on picture for examples worked out
Image from: //upload.wikimedia.org/wikipedia/commons/c/ce/ChilkootPass_Slope.jpg
![Page 9: Remediation. Slope Find the slope of a line given two points: (3, 4) and (7, 8). m = (8 – 4)/(7 – 3) = 4/4 = 1 The slope is 1](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f335503460f94c4f6eb/html5/thumbnails/9.jpg)
Assignment, continued
Find the equation of the line that passes through:
5) (6, 4) and m =
6) (-2, 7) and m =
3
2
5
3
6
35
5
3.6
3
2.5
xy
xy
Start with y=mx + b
![Page 10: Remediation. Slope Find the slope of a line given two points: (3, 4) and (7, 8). m = (8 – 4)/(7 – 3) = 4/4 = 1 The slope is 1](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f335503460f94c4f6eb/html5/thumbnails/10.jpg)
Assignment, continued
Find the equation of the line that passes through the points:
7) (-8, -6) and (0, -6)
8) (1, -6) and (7, -4)
9) (-8, 3) and (0, 0)
10) (17.5, -9) and (17.5, 13)
5.17.108
3.9
3
19
3
1.8
6.7
x
xy
xy
y
Click on picture for examples worked out
Image from: http://commons.wikimedia.org/wiki/File:Artificial_ski_slopes.JPG
![Page 11: Remediation. Slope Find the slope of a line given two points: (3, 4) and (7, 8). m = (8 – 4)/(7 – 3) = 4/4 = 1 The slope is 1](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f335503460f94c4f6eb/html5/thumbnails/11.jpg)
Graphing Lines
When a line is in slope intercept form, y=mx + b, you can graph by using the slope and the intercept.
Start by labeling your m (slope) and b (y-intercept).
Plot the b and move (rise/run) for the slope.
![Page 12: Remediation. Slope Find the slope of a line given two points: (3, 4) and (7, 8). m = (8 – 4)/(7 – 3) = 4/4 = 1 The slope is 1](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f335503460f94c4f6eb/html5/thumbnails/12.jpg)
Rise
Run
Graphing Linesy= 2x + 4y= 2x + 4
![Page 13: Remediation. Slope Find the slope of a line given two points: (3, 4) and (7, 8). m = (8 – 4)/(7 – 3) = 4/4 = 1 The slope is 1](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f335503460f94c4f6eb/html5/thumbnails/13.jpg)
Examples A 6-inch scented candle
burns at a rate of 0.1 inches each hour.
Starting at 6 inches= y-intercept, Decrease 0.1= slope -0.1
Let x=hours that the candle burns, y=height of the candle
*EQ: y=-0.1x+6 *Notice that the slope is negative because the candle height is decreasing as it burns!
*Q: How many hours has the candle burned if it is now 3.4 inches tall?
A: Use y=3.4, so 3.4=-
0.1x+6
-2.6=-0.1x, so x = 26 hours the candle burned
A national park has 8000 deer. It is estimated that the deer population will increase by 70 deer each year thereafter.
Starting 8000 = y-intercept, Increase 70 = slope
Let x=years from now, y=total deer in park
*EQ: y=70x+8000
*Q: How many deer will be in the park in 5 years?
A:Use x=5, so y=70(5)+8000=8350 deer in 5 years
![Page 14: Remediation. Slope Find the slope of a line given two points: (3, 4) and (7, 8). m = (8 – 4)/(7 – 3) = 4/4 = 1 The slope is 1](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f335503460f94c4f6eb/html5/thumbnails/14.jpg)
Find the intercepts (page will check your answers)
http://www.algebrahelp.com/worksheets/view/graphing/intercepts.quiz
Interactive Slope Slider
http://www.shodor.org/interactivate/activities/SlopeSlider/
Slope Quiz
http://cs.selu.edu/~rbyrd/math/slope/slo_ty.html
Practice
![Page 15: Remediation. Slope Find the slope of a line given two points: (3, 4) and (7, 8). m = (8 – 4)/(7 – 3) = 4/4 = 1 The slope is 1](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f335503460f94c4f6eb/html5/thumbnails/15.jpg)
Remediation LinksOverview
http://www.mathopenref.com/coordlineintro.html
Slope
http://www.mathopenref.com/coordslope.html
Point-Slope Form
http://www.mathopenref.com/coordequationps.html
Slope-Intercept Form
http://www.mathopenref.com/coordequation.html