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# Worked example: slope from two points

Find the slope of the line that goes through the ordered pairs (4,2) and (-3, 16). Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• Do I HAVE to use this method, or is it okay to just use the other one in the previous video, "Graphical Slope of a Line"? Is there really any difference?
• The method of graphing the line and then measuring the slope of the graph isn't a very good method when you are dealing with messy numbers (fractions, irrational numbers etc.) Also, the method used in this video will work even if you don't have graph paper.
• but if you do like Sal did - simplifying 14/-2 to -2
i can't figure out the slope!!
• Remember that -2 can be written like -2/1. :) Since -2 divided by 1 is just -2.

Do you see the rise over run now? -2 is the "rise", while 1 is the "run".

14/-7 is a proportional fraction to -2/1. You can simplify the fraction by dividing both numbers by 7.

14 divided by 7 is 2, and -7 divided 7 is -1. So, 14/-7 is equal to -2/1.

Since they are proportional fractions, their slope is actually the same too! :)

Let's try with Sal's examples, the starting point at (-3,16) to the ending point (4,2). With the rise over run -2/1 (which is the same as 14/-7 remember? Just simplified), we go 2 down and 1 right. Our starting point is now at (-2,14).

Let's go 2 down and 1 right again. Our point is now (-1,12).

Again. (0,10).

Again. :P (1,8)

Almost there. (2,6)

You see it? (3,4)

Well what do you know, now we are at (4,2)! The ending point we were aiming for.

Now, if you drew a line through all the coordinates we just made, it would look just like the line Sal drew. In fact, his line went through all the points that we made!

Try it yourself if you really care :P. Also, I'm sure you meant -7 right XP?
• How do you find the slope of a curved line?? (not linear)
• There is no such thing as the "slope of a curve" per se; what you have to find is the slope of the line that hugs the curve closely at a given point, called the tangent line at that point. You can find this by taking the derivative of the equation of the curve and then plugging in the x value of that point. That's the very beginning of calculus; you can watch Sal's videos on taking derivatives in the Calculus section. ^_^
• What happens if you already have the line, and need the ordered pairs?
• Watch the "Slope of a line" video. (The one before this one). The whole video is about finding slope WITHOUT needing the ordered pairs.
• How do you draw a slope on a graph when the only number you are given is the slope? Say the problem says "show the slope of 2." How would you know how to draw the line without any coordinates?
• Janine,
You can drawn it anywhere on the graph. Just choose any first point. Then go up two and right 1 for the second point and draw a line through the two points. Your line will have a slope of 2.
• 1. Do you have to draw an arrow head at each end of the line (see )? In other words, is this a "line" in the geometrical sense? Or is it a line segment? Or perhaps a ray that goes from (-3,16) to (4,2)?

I am thinking about the way he describes it as y decreases when x increases. I am also thinking about what it means that x is independent and y is dependent variable. Can you really go in either direction on the x in this situation?

2. How do you explicitly tell on a Cartesian plane that you are only investigating the change in x in the positive direction? Can you draw the x axis as a ray with only an arrow head at the right side and a point on the left side?
• 1. the question is ''find the slope of the line ''
so, yes it is a line in the geometrical sense.. and the line passes through the 2 points given

the equation of a line is y= mx +c
where y is dependent on x, m and c are constants and x is independent
and yes, you can go in both directions.. recall that a line goes on to infinity.. so, in principle there is no defined start point (therefore no start x-coordinate)
if x 'starts' from negative infinity and starts increasing, it is understood that it goes in both directions (positive and negative)

2. I'm not sure how to explain this one.. have you already watched the other videos?
• How can you explain it more simply because I am still struggling to understand?
• Hey there snoman! When finding slope of any 2 ordered pairs, for instance lets just use (2,9) and (19,10), a simple and quick method you can use is y2-y1 over x2-x1. Then just make sure you divide the y over the x in the end. Let me further explain using my example in 3 straightforward steps:

Step 1: You take the ordered pairs (2,9) and (19,10) and take out the y2 and y1 numbers. That would be 10 and 9. Then take out the x2 and x1 numbers. That should be 19 and 2.

Step 2: Next, you should minus the y2 and y1 numbers from each other. Your answer should be 1. After you do that, repeat the same process with the numbers of x2 and x1 and subtract both. Your answer should be 17.

Step 3: Final one! This is very important so you get your slope! Now, we have to use the method of rise/run or y change over x change to get the final answer. Divide your y number (1) over your x number (17). Your final answer should be 1/17.
• does it matter which sets of coordinates ((4,2) or (-3,16)) you start with?
• It does not matter which point you make (x1, y1) vs (x2, y2). If your math is correct you get the same result. So, just pick one to start with and label it (x2, y2). Then label the other point (x1, y1). You're then ready to map the numbers into the formula: m = (y2-y1) / (x2-x1).

Hope this helps.
• Instead of using y2-y1 over x2-x1, is it possible to use y1-y2 over x1-x2? Does it make a difference which one is used?
• It doesn’t matter at all, just as long as you have the same format, for example, if you do y2-y1, you have to keep that same format for x: x2-x1
• How does the slope work, if we are using 1 point, a slope, and the y variable, how do we find the other point without just choosing one?
• It sounds like you are trying to figure out how to graph a line given a point and the slope.
1) Graph the point that you know.
2) The slope is always "change in Y" / "change in X" and it tells you exactly how to move to find more points on the line. For example, if the slope is 3/4, the change in y = 4, so you go up 4 units. The change in X = 3, so you then move right 3 units. That is the location of another point on the line.

Hope this helps.