Slope – Intercept Form y = mx + b m represents the slope b represents the y-intercept.
Slope-Intercept Form y=mx + b. Slope Recall the three methods we can use to find slope.
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Transcript of Slope-Intercept Form y=mx + b. Slope Recall the three methods we can use to find slope.
![Page 1: Slope-Intercept Form y=mx + b. Slope Recall the three methods we can use to find slope.](https://reader033.fdocuments.in/reader033/viewer/2022051401/56649ea25503460f94ba565a/html5/thumbnails/1.jpg)
Slope-Intercept Form
y=mx + b
![Page 2: Slope-Intercept Form y=mx + b. Slope Recall the three methods we can use to find slope.](https://reader033.fdocuments.in/reader033/viewer/2022051401/56649ea25503460f94ba565a/html5/thumbnails/2.jpg)
Slope
Recall the three methods we can use to find slope.
bmxy
xx
yym
run
risem
12
12
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Slope
And recall the 4 types of slope
Positive Slope Negative Slope Slope of Zero Undefined Slope
Increases Left to Right
Decreases Left to Right
Horizontal Line Vertical Line
y = 3x + 2 y = - 3x + 2 y = 3 x = 5
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Slope
There are 3 methods we can use to find slope!
Each one works best for certain situations.
bmxy
xx
yym
run
risem
12
12
Remember this guy?
![Page 5: Slope-Intercept Form y=mx + b. Slope Recall the three methods we can use to find slope.](https://reader033.fdocuments.in/reader033/viewer/2022051401/56649ea25503460f94ba565a/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: Slope-Intercept Form y=mx + b. Slope Recall the three methods we can use to find slope.](https://reader033.fdocuments.in/reader033/viewer/2022051401/56649ea25503460f94ba565a/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 month
per
…a day
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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 originalstarting
where x = 0 (flat) fee
one time cost of one item
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You Try!
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xy 4
62
3 xy
8 xy
5 xy
Find the slope and y-intercept for the following equations
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xy 4
62
3 xy
8 xy
5 xy
0int,4 ym
6int,2
3 ym
8int,1 ym
5int,1 ym
How did you do?
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Graphing
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When given an equation like y = -3x + 2
You can graph the line by following these simple steps:
![Page 13: Slope-Intercept Form y=mx + b. Slope Recall the three methods we can use to find slope.](https://reader033.fdocuments.in/reader033/viewer/2022051401/56649ea25503460f94ba565a/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: Slope-Intercept Form y=mx + b. Slope Recall the three methods we can use to find slope.](https://reader033.fdocuments.in/reader033/viewer/2022051401/56649ea25503460f94ba565a/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)
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(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: Slope-Intercept Form y=mx + b. Slope Recall the three methods we can use to find slope.](https://reader033.fdocuments.in/reader033/viewer/2022051401/56649ea25503460f94ba565a/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 3/1
3)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: Slope-Intercept Form y=mx + b. Slope Recall the three methods we can use to find slope.](https://reader033.fdocuments.in/reader033/viewer/2022051401/56649ea25503460f94ba565a/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
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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.
14
5
14
5
212
38
212
)3(8
m
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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)
b
b
b
bmxy
34
362
)9)(4(2
b
b
b
b
b
b
bmxy
4
17
417
498
44
9424
4
92
)9(4
12
344 xy4
17
4
1 xy
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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)
17
2868
1128517
13826
m
m
m
217
28
2817
2826
1717
2826
)1(1
xy
xy
xy
xxmyy
So, what does this mean?(let’s “interpret” a look on the next slide)
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217
28 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 Variables
The 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 change
17
28
![Page 23: Slope-Intercept Form y=mx + b. Slope Recall the three methods we can use to find slope.](https://reader033.fdocuments.in/reader033/viewer/2022051401/56649ea25503460f94ba565a/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!