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