Question

Find the equation of a line that passes through the points (1,-5) and (3,-6).

Leave your answer in the form y =mx+c

Answer 1

y = -
`(1)/(2)` x -
`(9)/(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 =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (1, - 5) and (x₂, y₂ ) = (3, - 6)

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

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

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

Using (1, - 5 ) , then

- 5 = -
`(1)/(2)` + c ⇒ c = - 5 +
`(1)/(2)` = -
`(9)/(2)`

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