what is the equation of a line passing through (-4,-4) and (-8,-3)

Question

Using standard form Ax+By=C

Answer 1

A, B, and C are constants, so:

    -4A  - 4B  =  C           [use point (-4,-4)]

    -8A  - 3B  =  C           [use point (-8,-3)]

  --------------------     [elimination; subtract equation to get rid of C]

     4A  -B    = 0

     4A = B        [the coefficients have this proportion; use a point to solve for C]

 

  x + 4y = C                [proportion 1:4;   4A=B]

  (-4) + 4((-4) = C      [use either point]

     -20 = C

 

The equation, in Standard Format, is:

    x + 4y = -20

   

Answer 2

There's more than one way to solve this. I'm most comfortable with the slope-intercept form, so I will solve for that than convert to standard.

 

m = (y₂ - y₁)/(x₂ - x₁) = (-4 + 3)/(-4 + 8) = -1/4

 

y = mx + b

-4 = (-1/4)(-4) + b = 1 + b so b = -5

 

y = (-1/4)x - 5

 

Now, to get to standard form we must first get rid of fractions. So I multiplied everything in the slope-intercept equation by 4.

 

4y = -x - 20

 

Then added x to both sides.

 

x + 4y = -20

 

And that's it. Cheers!