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### Course: Algebra (all content)>Unit 3

Lesson 8: 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.

## Want to join the conversation?

• Why is slope referred by 'm'? Is it some kind of short form?
• The truth of it is, no-one really knows. There are several stories around that say it's the first letter for slope in various languages, or that it's derived from the Latin mons (which means mountain), but none of these has any evidence to substantiate them.
• 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?
• y-y1=m(x-x1)
• 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)
• my brain no comprendo
• 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!