Which equation represents the line that passes through points (1, -5) and (3,-17)?
o y=-6x+1
o y=6x+1
o y=-6x-1
o y=6x-1

y = - 6x + 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (1, - 5) and (x₂, y₂ ) = (3, - 17)

m = = = - 6, thus

y = - 6x + c ← is the partial equation of the line

To find c substitute either of the 2 points into the partial equation

Using (1, - 5), then

- 5 = - 6 + c ⇒ c = - 5 + 6 = 1

y = - 6x + 1 ← equation of line

-8/2y-8=5/y+4-7y+8/y^2-16

we move all terms to the left:

-8/2y-8-(5/y+4-7y+8/y^2-16)=0

we can not solve this equation