![Page 1: Module Four Lesson 2 Remediation Notes - Slope intercept form](https://reader035.vdocument.in/reader035/viewer/2022062821/589ee4bf1a28abe97f8b45ad/html5/thumbnails/1.jpg)
Slope-Intercept Form
y=mx + b
![Page 2: Module Four Lesson 2 Remediation Notes - Slope intercept form](https://reader035.vdocument.in/reader035/viewer/2022062821/589ee4bf1a28abe97f8b45ad/html5/thumbnails/2.jpg)
Slope
Recall the three methods we can use to find slope.
bmxyxxyym
runrisem
12
12
![Page 3: Module Four Lesson 2 Remediation Notes - Slope intercept form](https://reader035.vdocument.in/reader035/viewer/2022062821/589ee4bf1a28abe97f8b45ad/html5/thumbnails/3.jpg)
Slope
And recall the 4 types of slope
Positive Slope Negative Slope No Slope Undefined Slope
Increases Left to Right
Decreases Left to Right
Horizontal Line Vertical Line
y = 3x + 2 y = - 3x + 2 y = 3 x = 5
![Page 4: Module Four Lesson 2 Remediation Notes - Slope intercept form](https://reader035.vdocument.in/reader035/viewer/2022062821/589ee4bf1a28abe97f8b45ad/html5/thumbnails/4.jpg)
Slope
There are 3 methods we can use to find slope!
Each one works best for certain situations.
bmxyxxyym
runrisem
12
12
Remember this guy?
![Page 5: Module Four Lesson 2 Remediation Notes - Slope intercept form](https://reader035.vdocument.in/reader035/viewer/2022062821/589ee4bf1a28abe97f8b45ad/html5/thumbnails/5.jpg)
This is Slope Intercept Form.
We can use this equation to find the slope of a line and the y-intercept.
bmxy Remember this guy?
![Page 6: Module Four Lesson 2 Remediation Notes - Slope intercept form](https://reader035.vdocument.in/reader035/viewer/2022062821/589ee4bf1a28abe97f8b45ad/html5/thumbnails/6.jpg)
The slope is a constant but it is always affected by
something. The slope tells you the rate of change over each interval or time or an occurrence.
initial
…a yearevery
each …a monthper
…a day
![Page 7: Module Four Lesson 2 Remediation Notes - Slope intercept form](https://reader035.vdocument.in/reader035/viewer/2022062821/589ee4bf1a28abe97f8b45ad/html5/thumbnails/7.jpg)
The y-intercept is a constant.
This means that it is the starting point in a word problem, or a value that does not change and is not affected by
anything happening within the word problem.
initial originalstartingwhere x = 0 (flat) feeone time cost of one item
![Page 8: Module Four Lesson 2 Remediation Notes - Slope intercept form](https://reader035.vdocument.in/reader035/viewer/2022062821/589ee4bf1a28abe97f8b45ad/html5/thumbnails/8.jpg)
You Try!
![Page 9: Module Four Lesson 2 Remediation Notes - Slope intercept form](https://reader035.vdocument.in/reader035/viewer/2022062821/589ee4bf1a28abe97f8b45ad/html5/thumbnails/9.jpg)
xy 4
623
xy
8 xy
5 xy
Find the slope and y-intercept for the following equations
![Page 10: Module Four Lesson 2 Remediation Notes - Slope intercept form](https://reader035.vdocument.in/reader035/viewer/2022062821/589ee4bf1a28abe97f8b45ad/html5/thumbnails/10.jpg)
xy 4
623
xy
8 xy
5 xy
0int,4 ym
6int,23
ym
8int,1 ym
5int,1 ym
How did you do?
![Page 11: Module Four Lesson 2 Remediation Notes - Slope intercept form](https://reader035.vdocument.in/reader035/viewer/2022062821/589ee4bf1a28abe97f8b45ad/html5/thumbnails/11.jpg)
Graphing
![Page 12: Module Four Lesson 2 Remediation Notes - Slope intercept form](https://reader035.vdocument.in/reader035/viewer/2022062821/589ee4bf1a28abe97f8b45ad/html5/thumbnails/12.jpg)
When given an equation like y = -3x + 2
You can graph the line by following these simple steps:
![Page 13: Module Four Lesson 2 Remediation Notes - Slope intercept form](https://reader035.vdocument.in/reader035/viewer/2022062821/589ee4bf1a28abe97f8b45ad/html5/thumbnails/13.jpg)
When given an equation like y = -3x + 2
You can graph the line by following these simple steps:
1)Plot the y-intercept.(0,2)
![Page 14: Module Four Lesson 2 Remediation Notes - Slope intercept form](https://reader035.vdocument.in/reader035/viewer/2022062821/589ee4bf1a28abe97f8b45ad/html5/thumbnails/14.jpg)
When given an equation like y = -3x + 2
You can graph the line by following these simple steps:
1)Plot the y-intercept.
Notice that the slope is negative so the line must run from upper left to lower right!
(0,2)
![Page 15: Module Four Lesson 2 Remediation Notes - Slope intercept form](https://reader035.vdocument.in/reader035/viewer/2022062821/589ee4bf1a28abe97f8b45ad/html5/thumbnails/15.jpg)
(1,-1)
When given an equation like y = -3x + 2
You can graph the line by following these simple steps:
1)Plot the y-intercept.2)Use the slope to trace (rise / run) to the next point on the line. -3 is actually - 3/1
Notice that the slope is negative so the line must run from upper left to lower right!
(0,2)
![Page 16: Module Four Lesson 2 Remediation Notes - Slope intercept form](https://reader035.vdocument.in/reader035/viewer/2022062821/589ee4bf1a28abe97f8b45ad/html5/thumbnails/16.jpg)
When given an equation like y = -3x + 2
You can graph the line by following these simple steps:
1)Plot the y-intercept.2)Use the slope to trace (rise / run) to the next point on the line. 3 is actually 3/13)Connect the points with a line.
(1,-1)
(0,2)
Notice that the slope is negative so the line must run from upper left to lower right!
![Page 17: Module Four Lesson 2 Remediation Notes - Slope intercept form](https://reader035.vdocument.in/reader035/viewer/2022062821/589ee4bf1a28abe97f8b45ad/html5/thumbnails/17.jpg)
Review Problems
Given: The slope of a line is -2 and the y-intercept is 3. Write the equation of the line in slope-intercept form.
The information provided is enough for you to write the equation. m = -2, b = 3 and slope-intercept form isy = mx + b.
32 xy
![Page 18: Module Four Lesson 2 Remediation Notes - Slope intercept form](https://reader035.vdocument.in/reader035/viewer/2022062821/589ee4bf1a28abe97f8b45ad/html5/thumbnails/18.jpg)
Write the equation of the line in slope-intercept form that passes through the points: (2,-3) and (-12,-8).To write an equation in slope-intercept form we need the slope. 1.Use the ordered pairs to find the slope.
145
145
21238
212)3(8
m
![Page 19: Module Four Lesson 2 Remediation Notes - Slope intercept form](https://reader035.vdocument.in/reader035/viewer/2022062821/589ee4bf1a28abe97f8b45ad/html5/thumbnails/19.jpg)
![Page 20: Module Four Lesson 2 Remediation Notes - Slope intercept form](https://reader035.vdocument.in/reader035/viewer/2022062821/589ee4bf1a28abe97f8b45ad/html5/thumbnails/20.jpg)
Write the equation of the line in slope-intercept form that passes through the point (9,-2) and is
a)Parallel to y = -4x+7b)Perpendicular to y = -4x+7
Parallel Perpendicular
1. Slope of the parallel is -42. m = -4 and (9,-2)
1. Slope of the perpendicular is ¼ .
2. m = ¼ and (9,-2)
bbb
bmxy
34 362
)9)(4(2
b
bb
b
b
b
bmxy
417
417 498
449424
492
)9(412
344 xy4
1741 xy
![Page 21: Module Four Lesson 2 Remediation Notes - Slope intercept form](https://reader035.vdocument.in/reader035/viewer/2022062821/589ee4bf1a28abe97f8b45ad/html5/thumbnails/21.jpg)
Celia is out picking strawberries. She had 26 strawberries in her bucket after she had been picking for 17 minutes. She is now finished after spending 85 minutes picking. She has 138 strawberries.
Write an equation to model the number of strawberries, n, Celia picked per minute, t.
1. Independent and Dependent Variables
2. After you write the ordered pairs, find m.
3. Use the values to find the equation.
(Let’s practice with point-slope formula this time)
The number picked depends on the time spent picking.
Number is dependent on time, so the ordered pairs will look like: (t, n)
(17, 26) and (85, 138)
1728
68112
851713826
m
m
m
21728
28172826
17172826
)1(1
xy
xy
xy
xxmyy
So, what does this mean?(let’s “interpret” a look on the next slide)
![Page 22: Module Four Lesson 2 Remediation Notes - Slope intercept form](https://reader035.vdocument.in/reader035/viewer/2022062821/589ee4bf1a28abe97f8b45ad/html5/thumbnails/22.jpg)
21728
xy
We determined that the number of strawberries she had depended on the amount of time she had been picking.
The slope, 28/17, is the change in “y” or dependent value, which is n in this case over the change in “x” or the independent value, which is t in this case.
So we can say that
1. Independent and Dependent VariablesThe number picked depends on the time spent picking.
Number is dependent on time, so the ordered pairs will look like: (t, n) minutesin change
esstrawberri of #in change1728
![Page 23: Module Four Lesson 2 Remediation Notes - Slope intercept form](https://reader035.vdocument.in/reader035/viewer/2022062821/589ee4bf1a28abe97f8b45ad/html5/thumbnails/23.jpg)
Interpret slope : for every 17 minutes she picked 28 strawberries.
Or, if we find the unit rate by dividing, we get 1.647, which means for every 1 minute she picked about 1.647 strawberries.
Interpret y-intercept : she began with -2 strawberries. This is not realistic!