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## College Algebra

### Course: College Algebra > Unit 2

Lesson 3: Graphing from slope# Graphing a line given point and slope

Practice graphing a line given its slope and a point the line passes through.

## Want to join the conversation?

- how do you do fractions(20 votes)
- As a slope? you just need to remember rise over run. so if you had a fraction a/b where a and b are two numbers the slope is up by a and right by b, rise over run.

if the slope is negative then your rise is negative, so you go down. or you could look at it as your run being negative so you go left. either way, the other is normal. so negative slope means either the rise goes down and run goes right OR rise goes up and run goes left.

Let me know if that didn't help.(34 votes)

- upvote if u here in 2022(25 votes)
- why do we use (Y/X)coordinates instead of using (X/Y)?(8 votes)
- First of all, why do we consider something in the Y-axis and something else in the x-axis,

by convention, the value of y (or f(x)) is dependent on the value of x right?

so, the x-axis is generally considered as the independent value while the y-axis is the dependent value. (especially prevalent in physics, think of time(at least for classical mechanics), always in the x-axis cuz it doesn't depend on anything else,

now that we got that covered,

what does slope really mean?

=== what is the change in y values with change in the x values,

if the slope is 3 we can say: the y value changes by 3 for every change in 1 unit in x value,

it shows us the dependence of the dependent(y) and independent(x) values.

we don't say a change in x/change in y as that doesn't really help us as we go further,*why?*

alright, what does this*really*say?

=== what is the change in x to change in y? Does this really make sense?

well, not really as it doesn't provide valuable information as *y is depending on x, not the other way around!*

Thi concept proves very powerful as you learn calculus (literally, completely based on this simple, beautiful concept),

quick spoiler, using differential calculus, you'd be able to find the slope for even a curved graph! This can help you find sooooo many stuff like the instantaneous velocity, etc, etc,!, using Integral calculus (closely inked to differential calculus), you can find the area under a graph and understand why and what that area provides!

If you remember and understand this simple concept, it would be much easier (and more fun!) to understand the beautiful world of calculus, this is a basic, understand it well.

If anything I've written is wrong or misleading, do let me know :)

Hope this helps!

Onwards!

PS: I felt compelled to answer this question not only cuz it's an important basic but also due to the misleading 'answers' in the comment session (quite uncommon here in the KA community actually) of your question that indicate it is how it is,

there is always a reason why (especially in math),

keep questioning!(11 votes)

- Im still confused after watching this video(8 votes)
**Rewatch**it once more.(4 votes)

- In a given slope which is (-), I keep stumbling on if the numerator or denominator should be (-) when applying to initial coordinance.

For instance, I had to graph (-7,-4) with a slope of -2/3. I chose to make the 3 in 2/3 the negative number, but it was the 2 which should have been negative. Is there a consistent rule? It seems I've seen it both ways.(6 votes)- It really does not matter as long as you move in the correct direction. So a slope of -2/3 would go down 2 right 3, and if you applied the negative to the 3 (2/-3), you go up 2 left 3, all points should then be along the same line.

So with (-7.-4) you could go <3,-2> to get to (-4,-6), or you could go <-3,2> to get to (-10,-2).

Same if it is a positive slope, I could go up and to the right (2/3), or I could go down and to the left (-2/-3=2/3).(4 votes)

- The graph will not let me plot the coordinate, because the coordinate is on the very edge line.(5 votes)
- Can I also solve it by setting up a slope equation and finding the y-intercept from there? For example, using the question from the video:

y = -3

x = 4

-3 = -2(4) + b

-3 = -8 + b

-3 + 8 = -8 + 8 + b

5 = b

So our slope equation in completed form is y = -2x + 5. Hence, we can graph it by plotting (4,-3) and connecting it to (0,5), our y-intercept. I find this method quite convenient for me.(3 votes)- That will work fine, you are doing it more algebraically rather than graphically.(4 votes)

- what is slope(3 votes)
- Slope is the change in y over change in x.

To make things easier, it basically is

ex) Slope of point (3 , 5) and point (-2 , -6)

Lets say 5 and -6 is y in both points, and 3 and -2 is x,

you just have to do 5-(-6) over 3-(-2) which is 11/5.

or you can do -6-5 over -2-3 which is -11/-5, or 11/5.(4 votes)

- How do you find the slope?(2 votes)
- To find the slope(m), you would use the rise/run formula.

Or:

m = (y2 - y1) / (x2 - x1)

For example, let's say I have two points, (1,2) and (4,8). One point would be (x1,y1) (it doesn't matter which one you pick), and the other would be (x2,y2).

(1,2) = (x1,y1)

(4,8) = (x2,y2)

m = (y2 - y1) / (x2 - x1)

--> Substitute

m = (8 - 2) / (4 - 1)

--> Simplify

m = 6/3

m = 2 <-- Answer!

If you'd like to watch a video on the topic, here it is:

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs/x2f8bb11595b61c86:slope/v/slope-of-a-line-2(4 votes)

- As a slope? you just need to remember rise over run. so if you had a fraction a/b where a and b are two numbers the slope is up by a and right by b, rise over run.

if the slope is negative then your rise is negative, so you go down. or you could look at it as your run being negative so you go left. either way, the other is normal. so negative slope means either the rise goes down and run goes right OR rise goes up and run goes left.(3 votes)

## Video transcript

- [Instructor] We are told graph a line with the slope of negative two, that contains the point
four comma negative three. And we have our little Khan
Academy graphing widget right over here, where
we just have to find two points on that line, and then that will graph the line for us. So pause this video and even
if you don't have access to the widget right now, although it's all
available on Khan Academy, at least think about how
you would approach this. And if you have paper and pencil handy, I encourage you to try to
graph this line on your own, before I work through it
with this little widget. All right, now let's do it together. So we do know that it contains point four comma negative three. So that's I guess you
could say the easy part, we just have to find the point x is four y is negative three. So it's from the origin four
to the right, three down. But then we have to figure out
where could another point be? Because if we can figure
out another point, then we would have graphed the line. And the clue here is that they
say a slope of negative two. So one way to think about it
is, we can start at the point that we know is on the line,
and a slope of negative two tells us that as x increases
by one, y goes down by two. The change in why would be negative two. And so this could be
another point on that line. So I could graph it like
this is x goes up by one, as x goes from four to five, y will go, or y will change by negative two. So why we'll go from negative
three to negative five. So this will be done, we
have just graphed that line. Now another way that you could do it, because sometimes you might
not have space on the paper, or on the widget to be
able to go to the right for x to increase, is to go the other way. If you have a slope of negative two, another way to think about
it is, if x goes down by one, if x goes down by one,
then y goes up by two. 'Cause remember, slope is
change of y over change in x. So you could either say
you have a positive change in y of two when x has
a negative one change, or you could think of it when
x is a positive one change, y has a negative two change. But either way notice,
you got the same line. Notice this line is the same thing, as if we did the first way
is we had x going up by one and y going down by two, it's the exact same line.