With two given points, how do you get the answer for point slope form, slope intercept, and standard?

Question

For example if I were to have the points (6, 2), and (-7, 4) how would I solve it step by step

Answer 1

Hi, Sue.

 

Since you have two points, the first thing to do is find the slope of the line. (Slope is often written as m)

The slope formula is:

 

   y₂-y₁                    

   x₂-x₁                      

 

(also known as "the difference of the y coordinates over the difference of the x coordinates")

 

The slope for the given points is (4-2) / (-7 - 6) which equals - 2/13.

 

POINT-SLOPE FORM

 

(y - y₁) = m(x - x₁)       The x₁ and y₁ stand for coordinates of a point; x and y are part of the equation

 

(y - 2) = (- 2/13)(x - 6)    That's it!

 

SLOPE-INTERCEPT FORM

 

y=mx + b          To get this one, simplify the equation above. 

 

y - 2 = -2x/13 + 12/13

 

y = -2x/13 + 38/13

 

STANDARD FORM

 

Ax + By = C      

In this form, we want A,B & C to be integers, so we are going to multiply the previous equation by 13 to get rid of the denominator. (A should be positive as well.)

 

13y = -2x + 38    Then move the x term to the other side

 

2x + 13y = 38

 

 

 

Hope this helps!

Kathye P.