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

Question

I dont understand 

Answer 1

Hi Lovely:

 

We have two points and want to find the equation of the line.

First find the slope ..  m = (change in y)/(change in x)

(−2, 5), (6, −6)

m = (-6-5)/(6-(-2)) = -11/8

 

In point slope format of y = mx +b

where m = slope   and   b = y-intercept   the equation is:

y = (-11/8)x + b

 

Pick one of the given points to use as (x,y) and solve to find b.

Let's use (-2,5)

5 = (-11/8)(-2) + b

5 = 11/4 + b

5 - 11/4 = b

20/4 - 11/4 = b

9/4 = b

 

In point slope format the equation is:  y = (-11/8)x + 9/4

 

We want this in standard form of   ax + by = c

so add (11/8)x to both sides

 

(11/8)x + y = 9/4

 

To clear the fractions multiply through by 8

Final answer:

11x + 8y = 18