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Point-slope form

# Intro to point-slope form

Point-slope is the general form y-y₁=m(x-x₁) for linear equations. It emphasizes the slope of the line and a point on the line (that is not the y-intercept). Watch this video to learn more about it and see some examples. Created by Sal Khan.

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• Wait then what form is y = mx + b
• just a reorganized version of point-slope.. they say the same thing, just with different parts.
• At about seconds or so. He says that those triangles are the deltas. I understand that but for full formula for slope does it matter which y or x goes first? Would you still get the same answer?
• Slope is always rise over run. It doesn't matter which one you find first, but make sure they're in the proper place.

Consider a line with rise 5 and run 4. The rise/run way is 5/4. But the run/rise way is 4/5. That is a different value, and would give us with a completely different line.
• I am a student teacher and I have difficulty in thinking about an activity that will lead to this subject. They want it to be a discovery activity that will also serve as a motivational activity for this lesson. I refered to books, but there's no discovery activity for this lesson. Do you have anything in mind?
• Hi, Paula. Here are some ideas:

1. One way to think about point-slope form is as a rearrangement of the slope formula.
If you ask your kids to manipulate `m = (y - k)/(x - h)`, perhaps one will come up with `(y - k) = m(x - h)`.

2. Another way to think about point-slope form is as a transformation of the canonical line `y = mx`: That is to say, `(y - k) = m(x - h)` is the end result of a vertical translation by k units, and a horizontal translation by h units, performed in either order.

3. Also food for thought: Given a point `(h,k)` and a slope `m`, the equation
`(y - k) = m(x - h)` is guaranteed to evaluate as `0 = m·0 = 0`.
Of course 0 is the product of any number and 0. This conceptually echoes how polynomial factors yield roots, based on the fact that any zero product must have one or more zero factors (aka the Zero Product Property).
• what is the traditional point-slope formula?
• My math teacher uses an equation of y-y1 = m(x-x1). Is this equation equal to the one in the video? If so, what would the (a,b) be taking the place of?
• Yes they are the same, and (a,b) would take the place of (x1,y1)
• I don't understand pointform at all please explain someone
• The point-slope form is very useful when you don't have your y-intercept. It is used to write equations when you only have your slope and a point.
Point-slope form: y-a = m(x-b).
For example, your slope (m) is 3 and your point (a,b) is 9,10.
You would substitute your y-coordinate for a, and your x- coordinate for b. Your new equation would look like this: y-10 = 3(x-9). If you simplify this, then you will get your basic slope-intercept form: y=mx+b! I hope this made sense!
• what would i replace M with
• m in here is the slope or gradient. The way I find easier to think about it is how much y increases or decreases per change of one position in x.
Hope this wasn't too confusing!
• Why is slope referred by 'm'? Is it some kind of short form?
• It is not known why the letter m was chosen for slope; the choice may have been arbitrary. John Conway has suggested m could stand for "modulus of slope." One high school algebra textbook says the reason for m is unknown, but remarks that it is interesting that the French word for "to climb" is monter. The earliest known use of m for slope is an 1844 British text by Matthew O'Brien entitled "A Treatise on Plane Co-Ordinate Geometry"
• This is so confusing!! I just don't understand.