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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 •  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.
• upvote if u here in 2022 • why do we use (Y/X)coordinates instead of using (X/Y)? • 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!
• Im still confused after watching this video • 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. • 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).
• The graph will not let me plot the coordinate, because the coordinate is on the very edge line. • 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. • what is slope   