Question

What is the equation of a line that passes through the points (3, 6) and (8,4)?

y-2/x-2/2
y-2/x-27
y=-x-24
y=-x+36

Answer 1

4th option

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 ) = (3, 6 ) and (x₂, y₂ ) = (8, 4 )

m =
`(4-6)/(8-3)` =
`(-2)/(5)` = -
`(2)/(5)` , then

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

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

using (8, 4 ) , then

4 = -
`(2)/(5)` (8) + c = -
`(16)/(5)` + c ( add
`(16)/(5)` to both sides )

`(20)/(5)` +
`(16)/(5)` = c , that is

c =
`(36)/(5)`

y = -
`(2)/(5)` x +
`(36)/(5)` ← equation of line