Calculus is a branch of mathematics that deals with the study of continuous change and motion. It is divided into two main areas: differential calculus and integral calculus.
The passage provides insights about lines, curves, and the slope.. Lines are described as being straight
with a slope, and one needs to know the slope in order to graph a line. Curves are described as having a
slope, and the slope is what is important when graphing a curve.. The passage also provides examples of
how to find the slope of a line and how to create a formula for the slope. One 1 if this is the point x1 y1.
How far is that yeah it ‘s x1 for sure how far is this point yeah okay is within this budget if you ‘re all right
so far if you ‘re not Gilligan. Some we okay or no all right. If this was like the point of 3 Comma 5 to get
to 3. Comma 5. You go over 3 and up five right so then this would be three. This is not 3. 12 5. It ‘s x1 y1,
So we ‘re going over x1. How far are we going up good and here now When we talk about smoke
typically a long time ago. When you ‘re first introduced the slope. The teacher probably said yeah. It ‘s
how your line Rises or Falls, but then they also said slope is defined as 1 over what let ‘s go ahead. Let’s
try to identify what our Rises and what our run is what would you say would be our rise this way this
way so if we find the difference between those two numbers over there, we ‘re going to find the rise for
our line. What is the difference between those two numbers over there. How do you find the difference
this distance? Here right sure yeah if this was 10 and this was 3. The distance between them would be
what okay you ‘d subtract it right you do 10 minus 3. So here we ‘re going to go well. It ‘s not 10 and 3
its y2 and y1. So our rise we ‘re going to call y2 minus 1 1. Can we do the same thing with the run. How
far is our run. What ‘s that distance represent the representatives taking you-one I thought you ‘re going
to answer you instead you sneezed. I was like she’s off and then John it it ‘s a pretty good one yeah. We
got x2-x1 for sure sound familiar yeah. If we use the letter instead of the word slow what letter-am I
talking later we use em and step slope. We got our formula we. Our formula we ‘re just kind of you ‘ve
seen it before right you probably saw anything invented before like this. If you have n’t well something
new for you have well you’ve seen it again. This is how you invent the slope formula. The reason why we
couldn’t use specific points is because we want to be able to plug in any two points that I give you right
so using that if you call your points X1 Y1-x2 Y2, you can find a slope for anything now the one reason
why I invent this for you is I want to show you. The passage discusses how to find the line equation for a
specific set of points.. The author mentions that by fixing one point, they are able to transform the
equation into a form that is easier to work with. Additionally, the author mentions that slope. Is named
after what is needed to calculate it..
We ‘re going to go through some families of curves. We’ll give you some trig functions your favorite
right and then we ‘ll get to the capital itself lots of weird minds. What do you know about a line?. We’ll
talk about how to find the slope of a line and invent the formula ourselves so let’s take a generic line
and we’ll pick two random points. If we find the difference between those two numbers over there we
‘re going to find the rise for our line. How far is this point. How far is within this budget. If you ‘re not
gilligan some we okay or no all right. If this was like the point of 3 Comma 5 to get to 3 Comma5. You go
over 3 and up five right so then this would be three. This is not 3 12 5. It ‘s x1 y1. So we ‘’re going over
X1, How far are we going up good and here now when we talk about smoke typically a long time ago.
When you “re first introduced the slope. The teacher probably said yeah it ‘’s how your line r we ‘re
going to be able to get the formula for lines. So here ‘s going to work with we’re going to start with m
equals Y2 minus y1 over x2 minus x1. We fixed only one point and let the other one float what that does
is it changes this formula.
, I know you were n’t doing math over Christmas break we ‘re or holiday break whatever you ‘re doing
what are you doing math. I was I was redoing this class to make an extra super special for you. You
should feel honored, but let ‘s go ahead and try to find the equation of the line passes through these
two points. A quick show hands how many people were able to find the slope good start here but that ‘s
fine if you ‘re not work on that later okay revisit this try to follow through this example. See if you’re
doing it own and then come up that ½ I ‘ll be done we ‘re about halfway there. When we have y equals
mx plus b when we have some number times x plus or minus some constant. We know that that’s going
to be called with that. Is slopeintercept. It ‘s pretty easy to graph it gives you what you need to graph a
line very quickly and again. The reason why is slope intercept is that ‘s what you have that animal well
that’s our slope. What’s the B stand for..
Positive slope It would just change the sign. So let me show you how that would work if I picked
negative 2 for x1 and positive 2 for y1. What does that do to the slope. If I pick x1, y1, x2 and y2,
negative 2 for x1 and positive 2 for y2. Then what does that do to the slope It changes the sign so let’s
try this one another way so let’s say I pick x1 y1 x2 and y2 positive 2 for x1 and negative 2 for y2. What
does that do to the slope It makes it a positive slope. Now let’s try this one last one so let’s say I pick x1
y1 x2 and y2 negative 1 for x1 and positive 1 for y2. What does that do to the slope. It makes it a
negative slope okay so as far as the slope. Goes in this scenario, we would have a positive slope because
we changed the sign So let’s take a look at our equation right now. So we have y’=mx+b now let’s
subtract b from both sides we’re left with y’=-mx+b. So our equation of the line is y=-mx+b The passage
discusses how to graph a line. It states that to graph a line, one first has to identify the y-intercept and
slope. The y-intercept is the point at which the line crosses the y-axis, and the slope is the change in y-
values with respect to change in X-values. Once. These two values are identified, one can use them to
graph. The line. Slope-intercept is a line property that tells you where the line crosses the y-axis..
The Passage discusses how to create a horizontal line and a vertical line using a constant.. IT also
discusses how to find the slope and the y-intercept of a line. Using these methods. Yes, one can find a
parallel or perpendicular line using an equation. Minus 7 equals plus 6 and plus 6 divided by 2 equals 12,
so that’s our slope intercept for this line. We can just write it down and we’re done with our review
problem all right.
The Passage discusses how to create a horizontal line and a vertical line using a constant.. IT also
discusses how to find the slope and the y-intercept of a line. Using these methods. Yes, one can find a
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