Point slope form
The point slope form of a line is: y  y
_{1} = m (x  x
_{1}) m is the slope and (x
_{1}, y
_{1}) is a point on the line
This lesson will use the slope and a point that are given to write the equation of a line in this form
y  y
_{1} = m (x  x
_{1})
Example #1
Given m = 2 and (3, 4), write the point slope form
Notice that (x
_{1}, y
_{1}) = (3, 4)
Just replace the slope and the point into the formula using m = 2 and x
_{1} = 3 and y
_{1} = 4
After replacing the slope:
y  y
_{1} = 2 (x  x
_{1})
After replacing (x
_{1}, y
_{1}) :
y  4 = 2 (x  3)
Example #2
Given m = 8 and (3, 4)
Notice that (x
_{1}, y
_{1}) = (3, 4)
Just replace the slope and the point into the formula using m = 8 and x
_{1} = 3 and y
_{1} = 4
After replacing the slope:
y  y
_{1} = 8 (x  x
_{1})
common pitfall: forgetting to type the negative or the minus sign when replacing (x
_{1}, y
_{1})
Thus, make sure both the minus sign and the negative sign are included in the equation
After replacing (x
_{1}, y
_{1}) :
y  4 = 8 (x  3) (two negatives equals a plus in this case)
y  4 = 8 (x + 3)
Example #3
Given m = 10 and (5, 1)
Notice that (x
_{1}, y
_{1}) = (5, 1)
Just replace the slope and the point into the formula using m = 10 and x
_{1} = 5 and y
_{1} = 1
After replacing the slope:
y  y
_{1} = 10 (x  x
_{1})
After replacing (x
_{1}, y
_{1}) :
y  1 = 10 (x  5)
y + 1 = 10 (x + 5)
Sometimes, you might need to write tthe equation from point slope form to slope intercept form
Take the point slope form for example #3 for instance
y + 1 = 10 (x + 5)
y + 1 = 10 × x + 10 × 5
y + 1 = 10x + 50
y + 1  1 = 10x + 50  1
y = 10x + 51

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