Question

Find a equation for the line below

Answer 1

y = -
`(1)/(2)` x -
`(13)/(2)`

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 ) = (- 5, - 4) and (x₂, y₂ ) = (- 1, - 6)

m =
`(-6+4)/(-1+5)` =
`(-2)/(4)` = -
`(1)/(2)`, thus

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

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

Using (- 1, - 6), then

- 6 =
`(1)/(2)` + c ⇒ c = - 6 -
`(1)/(2)` = -
`(13)/(2)`

y = -
`(1)/(2)` x -
`(13)/(2)` ← equation of line