equations in point slope form

Question

Given the points (3, 3) and (0, -3), construct two equations in point slope form using each of the points. 

Answer 1

 

Point-slope formula is y - y₁ = m(x - x₁)

 

Where (x₁, y₁) is a point on the line, and m is the slope

 

The slope of the line is found using the slope formula ...

 

  m = (y₂ - y₁)/(x₂ - x₁)

      = (-3-3)/(0-3)

      = -6/-3

      = 2

 

So the slope of the line is 2.

 

Using Point (3,3)

   y - 3 = 2(x - 3) is the equation

 

Using Point (0,-3)

   y - (-3) = 2(x - 0)

   

 

Answer 2

The first step to point slope form is finding the slope.  Since we have two points, we can calculate this as change in y over change in x:

 

Δy/Δx = (3 - (-3)) / (3 - 0) = 6 / 3 = 2

 

Now that we know that our slope m = 2, we can choose either point and apply the same formula to create our point slope form.  Using the first point, we get:

 

Δy/Δx = m

(y - 3)/(x - 3) = 2

 

If we use the second point, we get:

 

(y - (-3))/(x - 0) = 2

(y + 3)/x = 2

 

Incidentally, if you were to solve both of these for y, you would get identical solutions y = 2x-3, because there's only one straight line that goes through both points.

 

If you have any further questions, please let me know.