Find the equation of the line containing the given pair of points (1,2) and(3,3)

Question

Find the equation of the line containing the given pair of points (1,2) and(3,3) 

Answer 1

First, determine which form of an equation to use for writing your answer.  If it is slope-intercept (y = mx + b), then use that with two points.  The points are P₁:  (1,2)   and P₂: (3,3)

 

The slope, m, is 'rise' over 'run,' or   (y₂-y₁)/(x₂-x₁), so plug that into the point-slope form:

                    y = [(y₂ - y1)/(x₂ - x₁)]x + b

                    y = [(3-2)/(3-1)]x + b

                     y = (1/2)x + b

 

Now, use either point to solve for b.  Let's use (1,2):

                  2 = (1/2)*1 + b

                   3/2  = b              (subtract 1/2 from both sides)

                   y = (1/2)x + 3/2

 

Checking (very important):

        Is 2 = (1/2)*1 + 3/2   ?    Yes, first point is on line.

        Is 3 = (1/2)*3 + 3/2   ?    Yes, second point is on line.

 

Answer 2

For questions like these when you are given two points, you should use the "point-slope" equation.

 

It is written as 

 

(y-y₁)=m(x-x₁),

 

where (x₁,y₁) is the point you would like to be on the line and m is your slope. And slope is calculated as "rise" over "run" or change in "y" over change in "x", which is

 

m=Δy/Δx=(y₂-y₁)/(x₂-x₁).

 

So with points (1,2) and (3,3), we would first calculate the slope as

 

m=Δy/Δx=(y2-y1)/(x2-x1)=(3-2)/(3-1)=1/2

 

And finally, using either point, you would plug your values in the "point-slope" equation and simplify. In my case, I used (3,3):

 

(y-3)=(1/2)(x-3)

 

y-3= x/2 -3/2

 

y=x/2 + 3/2

 

I hope this helped!