Question

Write an equation of the line that passes through the points (-1,-2) and (5,1)

Answer 1

Y=-1/2x ?

Explanation:

There might be an y intercept. First find the slope. (Change in y over change in x) -2-1 over -1-5 then you get -3/-6. You can simplify an get -1/2. That forms an equation of y=-1/2x. That might be part of the answer. You still might need to find the y intercept, and I dont know how really. Hope this helps.

Answer 2

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

Explanation:

the equation of a line in slope- intercept form is

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

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (- 1, - 2) and (x₂, y₂ ) = (5, 1)

m =
`(1+2)/(5+1)` =
`(3)/(6)` =
`(1)/(2)`, hence

y =
`(1)/(2)` x + c ← is the partial equation

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

using (- 1, - 2 ), then

- 2 = -
`(1)/(2)` + c ⇒ c = - 2 +
`(1)/(2)` = -
`(3)/(2)`

y =
`(1)/(2)` x -
`(3)/(2)` ← is the equation of the line