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How Do You Write an Equation of a Line in Point-Slope Form If You Have Two Points?

Write the point-slope form of the line going through (0,-2) and (3,4).

Summary

  1. Point-slope form is y-y1=m(x-x1)
  2. 'm' stands for slope
  3. (x1,y1) is a point on the line
  4. (x2,y2) is a different point on the line
  5. The slope is the difference in the y-coordinates over the difference in the x-coordinates
  6. We're defining (0,-2) as (x1,y1) and (3,4) as (x2,y2)
  7. 4-(-2) is the same as 4+2
  8. Even though we called (0,-2) (x1,y1) before, we can use either point when we plug into the point-slope formula

Notes

    1. Point-slope form is y-y1=m(x-x1)
    2. 'm' stands for slope
    3. (x1,y1) is a point on the line
    1. In order to write an equation in point-slope form, we need to figure out the slope!
    1. We can find the slope if we use the formula for slope with those two points
    1. The slope is the 'change in y' over the 'change in x'
    2. We can also think of this as the difference in the y-coordinates over the difference in the x-coordinates
    1. (x1,y1) and (x2,y2) are two points on the line
    2. This formula just gives us the difference in the y-coordinates over the difference in the x-coordinates
    1. We're defining (0,-2) as (x1,y1) and (3,4) as (x2,y2)
    2. This makes the slope equal to 4-(-2) divided by 3-0
    1. The slope is equal to 4-(-2) divided by 3-0
    2. 4-(-2) is the same as 4+2, or 6
    3. 6 divided by 3-0 is equal to 6 divided by 3, or 2
    1. Point-slope form is y-y1=m(x-x1)
    2. 'm' stands for slope, which we found to be 2
    3. (x1,y1) is any point on the line
    1. (x1,y1) can be any point on the line
    1. (x1, y1) is just any point on the line
    2. Since it can be any point, we can pick either point that we already know
    3. Even though earlier we called (0,-2), we are going to use (3,4) for the point (x1,y1) this time
    4. This is okay, because we can use any point on the line to write the equation!
    1. This time we're using (3,4) for the point (x1,y1)
    1. We found the line y-4=2(x-3)
    2. If we used a different point, like (0,-2) instead of (3,4), we would get an equation that looks a little different
    3. But if you solve the equation for y, you'd find that it's the same line!