Question

Write the equation of the line determined by the given pair of points in slope-intercept form. (-1,4) and (5,2)

Answer 1

y = -
`(1)/(3)` x +
`(11)/(3)`

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, 4 ) and (x₂, y₂ ) = (5, 2 )

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

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

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

using (- 1, 4 )

4 = -
`(1)/(3)` (- 1) + c =
`(1)/(3)` + c ( subtract
`(1)/(3)` from both sides )

4 -
`(1)/(3)` = c , that is

c =
`(12)/(3)` -
`(1)/(3)` =
`(11)/(3)`

y = -
`(1)/(3)` x +
`(11)/(3)` ← equation of line