Point slope form

The point slope form of a line is: y - y1 = m (x - x1)   m is the slope and (x1, y1) 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 - y1 = m (x - x1)

Example #1


Given m = 2 and (3, 4), write the point slope form

Notice that (x1, y1) = (3, 4)

Just replace the slope and the point into the formula using m = 2 and x1 = 3 and y1 = 4

After replacing the slope:

y - y1 = 2 (x - x1)

After replacing (x1, y1) :

y - 4 = 2 (x - 3)


Example #2


Given m = 8 and (-3, 4)

Notice that (x1, y1) = (-3, 4)

Just replace the slope and the point into the formula using m = 8 and x1 = -3 and y1 = 4

After replacing the slope:

y - y1 = 8 (x - x1)

common pitfall: forgetting to type the negative or the minus sign when replacing (x1, y1)

Thus, make sure both the minus sign and the negative sign are included in the equation

After replacing (x1, y1) :

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 (x1, y1) = (-5, -1)

Just replace the slope and the point into the formula using m = -10 and x1 = -5 and y1 = -1

After replacing the slope:

y - y1 = -10 (x - x1)

After replacing (x1, y1) :

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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