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To solve systems of equations by graphing, just simplify the equations to be in slope intercept form (y = mx + b), and then graph them. Finally, fi...
Please be advised that Shmoop does not endorse owning a pet Stegosaurus. The character in this video is a professional—do not attempt at home.
If we never put any points on our graphs, they’d really just be grids. Just sayin'.
How Slope Works 3347 Views
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- 00:00
we<00:00:01.560>
see <00:00:02.040>how <00:00:04.589> slope <00:00:05.040>works <00:00:05.490> a <00:00:05.819> lot - 00:14
alright<00:00:15.030> welcome <00:00:15.330> to <00:00:15.570>mount <00:00:15.870> up - 00:16
alright welcome to mount up - 00:16
alright welcome to mount up here's<00:00:16.740> a <00:00:16.800>line <00:00:17.130>with <00:00:17.279>a <00:00:17.369>slope <00:00:17.609> and - 00:18
here's a line with a slope and Full Transcript
- 00:18
here's a line with a slope and right<00:00:18.840> there <00:00:19.020>and <00:00:19.560>here <00:00:19.680>the <00:00:19.830>line - 00:19
right there and here the line
- 00:20
right there and here the line with<00:00:20.250>
a <00:00:20.279>slope - 00:21
with a slope
- 00:21
with a slope
what's<00:00:21.750> the <00:00:21.840> slow <00:00:22.109> of <00:00:22.650>this <00:00:22.920>guy <00:00:23.130>here - 00:24
what's the slow of this guy here - 00:24
what's the slow of this guy here well<00:00:24.720> we're <00:00:24.900> going <00:00:25.050> to <00:00:25.109>show <00:00:25.230>you <00:00:25.410>a - 00:25
well we're going to show you a - 00:25
well we're going to show you a little<00:00:25.650> magic <00:00:25.949> trick <00:00:26.400>don't <00:00:26.580>worry - 00:26
little magic
trick don't worry - 00:26
little magic
trick don't worry no<00:00:26.939> dogs <00:00:27.330>will <00:00:27.480>be <00:00:27.599>harmed <00:00:27.930>in <00:00:28.109>the - 00:28
no dogs will be harmed in the
- 00:28
no dogs will be harmed in the making<00:00:28.230>
of <00:00:28.619> magic - 00:29
making of
magic - 00:30
making of
magic alright<00:00:30.240> well <00:00:30.359>the <00:00:30.449>slope <00:00:30.750>of <00:00:30.840>the - 00:30
alright well the slope of the - 00:30
alright well the slope of the line<00:00:31.170> is <00:00:31.500>just <00:00:31.769>about <00:00:31.920>how <00:00:32.189>steep <00:00:32.820>or - 00:33
line is just about how steep or
- 00:33
line is just about how steep or flat
<00:00:34.380> it <00:00:34.530>is <00:00:34.649> there's <00:00:35.550>a <00:00:35.610>number - 00:35
flat
it is there's a number - 00:35
flat
it is there's a number associated<00:00:36.300> with <00:00:36.750>that <00:00:36.930>steepness - 00:36
associated with that steepness
- 00:37
associated with that steepness or<00:00:37.649>
flatness <00:00:38.160>called <00:00:38.489>es <00:00:38.910>you - 00:38
or flatness called es you
- 00:39
or flatness called es you
guessed<00:00:39.480> it <00:00:39.540>slow - 00:40
guessed it slow - 00:40
guessed it slow well <00:00:40.500> it's <00:00:40.649>usually <00:00:41.040>calculated <00:00:41.430>as - 00:41
well
it's usually calculated as - 00:41
well
it's usually calculated as a<00:00:41.850> fraction <00:00:42.300>of <00:00:42.570>the <00:00:42.750> Y <00:00:42.899>over <00:00:43.230> X <00:00:43.469>Orion - 00:43
a fraction of the
Y over X Orion - 00:44
a fraction of the
Y over X Orion fancy-pants<00:00:44.879> math <00:00:45.090>terms <00:00:45.480> it <00:00:45.780>looks - 00:45
fancy-pants math terms it looks - 00:45
fancy-pants math terms it looks like<00:00:46.140> this - 00:46
like this
- 00:47
like this
alright<00:00:47.760> so <00:00:48.120>to <00:00:48.210>get <00:00:48.300>the <00:00:48.450>slope <00:00:48.750>of - 00:48
alright so to get the slope of - 00:48
alright so to get the slope of the<00:00:48.930> line <00:00:49.110>you <00:00:49.500>just <00:00:49.559>subtract <00:00:50.250>this - 00:50
the line you just subtract this - 00:50
the line you just subtract this number <00:00:50.550> the <00:00:51.239>y <00:00:51.420>coordinate <00:00:52.020> for <00:00:52.230>the - 00:52
number
the y coordinate for the - 00:52
number
the y coordinate for the first <00:00:52.680> . <00:00:53.100> from <00:00:53.699>the <00:00:53.789>y <00:00:54.000>coordinate - 00:54
first . from the y coordinate - 00:54
first . from the y coordinate for<00:00:54.809> the <00:00:54.899>second <00:00:55.530> point <00:00:56.010>here <00:00:56.879> in - 00:57
for the second
point here in - 00:57
for the second
point here in this <00:00:57.809> case <00:00:58.109>we <00:00:58.230>have <00:00:58.350>this <00:00:58.500> 3 <00:00:58.920>minus - 00:59
this
case we have this 3 minus - 00:59
this
case we have this 3 minus this <00:00:59.730> 0 <00:01:00.239>and <00:01:00.930>the <00:01:01.020>top <00:01:01.320>number <00:01:01.500>in <00:01:01.770>the - 01:01
this
0 and the top number in the - 01:01
this
0 and the top number in the fraction<00:01:02.280> is <00:01:02.520> three <00:01:03.090>right - 01:03
fraction is
three right - 01:04
fraction is
three right halfway<00:01:04.470> there <00:01:04.589>now <00:01:05.100>to <00:01:05.369>calculate - 01:05
halfway there now to calculate - 01:05
halfway there now to calculate this<00:01:05.970> number <00:01:06.330>i'll <00:01:06.810> just <00:01:07.320>take <00:01:07.439>the - 01:07
this number i'll just take the - 01:07
this number i'll just take the first <00:01:08.010> X <00:01:08.310>here <00:01:08.549>which <00:01:08.820>is <00:01:08.970> 3 <00:01:09.360>and - 01:09
first
X here which is 3 and - 01:09
first
X here which is 3 and subtract<00:01:10.530> the <00:01:10.710>section <00:01:11.250> X <00:01:11.640>here - 01:11
subtract the section
X here - 01:12
subtract the section
X here which<00:01:12.510> is <00:01:12.720> zero <00:01:12.869>and <00:01:13.590>while <00:01:13.770>we <00:01:13.890>get - 01:13
which is
zero and while we get - 01:13
which is
zero and while we get three<00:01:14.250> again <00:01:14.520> so <00:01:14.970>our <00:01:15.060>slope - 01:15
three again so our slope - 01:15
three again so our slope fraction<00:01:15.960> is <00:01:16.110>just <00:01:16.350> 3 <00:01:16.530>over <00:01:16.770> 3 - 01:16
fraction is just
3 over 3 - 01:17
fraction is just
3 over 3 yes<00:01:17.880> the <00:01:18.000>loneliest <00:01:18.479>number <00:01:18.720> think - 01:19
yes the loneliest number
think - 01:19
yes the loneliest number
think one <00:01:19.950> all <00:01:20.640>right <00:01:20.700>but <00:01:21.210> what <00:01:21.360> if <00:01:21.450>we - 01:21
one all right but what if we - 01:21
one all right but what if we started<00:01:21.720> with <00:01:22.080>this <00:01:22.259> point <00:01:22.770>as <00:01:22.890>the - 01:22
started with this
point as the - 01:22
started with this
point as the first<00:01:23.400> one <00:01:23.610> the <00:01:23.850>origin <00:01:24.240>here <00:01:24.420> and - 01:24
first one
the origin here and - 01:24
first one
the origin here and subtracted <00:01:25.500> the <00:01:25.560>peak <00:01:26.130>which <00:01:26.700>now - 01:26
subtracted
the peak which now - 01:26
subtracted
the peak which now will<00:01:27.270> call <00:01:27.450> the <00:01:27.720>second <00:01:28.290>number <00:01:28.320> but - 01:28
will call the second number but - 01:28
will call the second number but with<00:01:29.130> the <00:01:29.220>slope <00:01:29.490>change <00:01:29.909> now <00:01:30.900>for - 01:31
with the slope change now for - 01:31
with the slope change now for the<00:01:31.740> numerator <00:01:32.220> y-coordinate <00:01:33.119>we - 01:33
the numerator
y-coordinate we - 01:33
the numerator
y-coordinate we have<00:01:33.600> 0-3 <00:01:34.770>to <00:01:35.220>get <00:01:35.369>negative <00:01:35.640> 3 <00:01:36.060> and - 01:36
have 0-3 to get negative
3 and - 01:36
have 0-3 to get negative
3 and then<00:01:36.659> we <00:01:36.780>do <00:01:36.900>the <00:01:36.990>same <00:01:37.380>for <00:01:37.500>the - 01:37
then we do the same for the
- 01:37
then we do the same for the
x-coordinate<00:01:38.340> here <00:01:38.520>and <00:01:38.790>get - 01:38
x-coordinate here and get - 01:39
x-coordinate here and get negative <00:01:39.840> 3 - 01:40
negative
3 - 01:40
negative
3 well<00:01:41.040> the <00:01:41.100>fraction <00:01:41.549>would <00:01:41.700>be <00:01:41.850>just - 01:41
well the fraction would be just - 01:42
well the fraction would be just negative<00:01:42.450> 3 <00:01:42.630>over <00:01:42.720>negative <00:01:42.899>3 <00:01:43.229>which - 01:43
negative 3 over negative 3 which - 01:43
negative 3 over negative 3 which in <00:01:43.829> California <00:01:44.430>is <00:01:44.700>yet <00:01:44.909>again <00:01:45.030>the - 01:45
in
California is yet again the - 01:45
in
California is yet again the loneliest<00:01:45.750> number - 01:45
loneliest number
- 01:46
loneliest number so<00:01:46.740>
the <00:01:46.860>slope <00:01:46.979>is <00:01:47.189> one <00:01:47.579>that <00:01:48.119>is <00:01:48.210>for - 01:48
so the slope is
one that is for - 01:48
so the slope is
one that is for each <00:01:49.079> Rock <00:01:49.590>we <00:01:49.799>move <00:01:50.220> ease - 01:50
each
Rock we move ease - 01:51
each
Rock we move ease way <00:01:51.330> as <00:01:51.750>we <00:01:51.930>climb <00:01:52.440> Mount <00:01:52.740>month <00:01:53.159>we - 01:53
way
as we climb Mount month we - 01:53
way
as we climb Mount month we also<00:01:53.640> rise <00:01:53.940>one <00:01:54.420> Rock <00:01:54.840>toward <00:01:55.200>the - 01:55
also rise one
Rock toward the - 01:55
also rise one
Rock toward the Sun <00:01:55.770> slope <00:01:56.700>of <00:01:57.210> one <00:01:57.540>pretty <00:01:58.170> good - 01:58
Sun slope of one pretty good - 01:58
Sun slope of one pretty good trick - 02:04
trick - 02:05
trick what <00:02:05.900> did <00:02:05.990>the <00:02:06.080> Buffalo <00:02:06.530>say <00:02:06.800>to <00:02:06.980>his - 02:06
what
did the Buffalo say to his - 02:07
what
did the Buffalo say to his son <00:02:07.610> as <00:02:07.730>he <00:02:07.850>left <00:02:08.149>for <00:02:08.420>school - 02:09
son
as he left for school - 02:09
son
as he left for school bye<00:02:09.860> son <00:02:11.660>okay <00:02:12.200>bad <00:02:12.410>joke <00:02:12.500>but <00:02:12.740>if <00:02:12.920>you - 02:12
bye son okay bad joke but if you - 02:13
bye son okay bad joke but if you survived <00:02:13.550> and <00:02:13.670>how <00:02:13.760>about <00:02:13.970>clicking - 02:13
survived
and how about clicking - 02:14
survived
and how about clicking the<00:02:14.510> subscribe <00:02:14.750>button <00:02:15.260>below <00:02:15.650> and - 02:16
the subscribe button below
and - 02:16
the subscribe button below
and if<00:02:16.700> you're <00:02:16.820>looking <00:02:17.090>for <00:02:17.150>more <00:02:17.360>jokes - 02:17
if you're looking for more jokes
- 02:17
if you're looking for more jokes from<00:02:17.840>
yours <00:02:18.290>truly <00:02:18.650>why <00:02:18.830>not <00:02:19.040>check - 02:19
from yours truly why not check
- 02:19
from yours truly why not check out<00:02:19.400>
our <00:02:19.550>website <00:02:19.880>at <00:02:20.180>wweshop.com - 02:20
out our website at wweshop.com
- 02:20
out our website at wweshop.com
if<00:02:22.430> you <00:02:22.550>want <00:02:22.700>to <00:02:22.760>get <00:02:22.820>updates <00:02:23.300>on - 02:23
if you want to get updates on - 02:23
if you want to get updates on what's<00:02:23.690> new <00:02:23.840>well <00:02:24.170>check <00:02:24.470>us <00:02:24.560>out <00:02:24.680>on - 02:24
what's new well check us out on
- 02:24
what's new well check us out on
facebook<00:02:25.040> and <00:02:25.520>to <00:02:26.000>please - 02:31
facebook and twitter to please - 02:31
facebook and twitter to please check<00:02:32.240> our <00:02:32.330>
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