Write the equation of the line that contains the indicated pair of points. Express the final equation in standard form. (2, 1), (6, 5)

Question

I don't understand 

Answer 1

(2, 1), (6, 5)

 

First find the slope of the line:

slope:  m = (change in y)/(change in x) = (5-1)/(6-2) = 4/4 = 1

 

Point slope form is:  y = mx + b

where m is slope and b is y-intercept

we know m=1  so we have y = x+b

 

Use either of the two given points as (x,y) and solve for b.

Let's use (2,1)

 

1 = 2 + b

1-2 = b

-1 = b

 

IN point slope form the equation is:  y = x -1

 

Standard form is  ax + by = c so subtract x from both sides

 

-x + y = -1    or   x - y = 1

 

Answer 2

slope M = (5-1)/(6-2) = 4/4 = 1

 

y = Mx + b

 

(2,1) --> x=2, y = 1, M= 1

 

1 = (1)(2) + b

 

1 = 2 + b

 

b = -1

 

the equation is y = x - 1

 

 

In standard form it is y  - x = -1