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