Question

Find the equation of the line passing through each pair of points.
a (1,0) and (5, 6)

Answer 1

y =
`(3)/(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 )

calculate m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

let (x₁, y₁ ) = (1, 0 ) and (x₂, y₂ ) = (5, 6 )

substitute these values into the formula for m

m =
`(6-0)/(5-1)` =
`(6)/(4)` =
`(3)/(2)` , then

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

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

using (1, 0 )

0 =
`(3)/(2)` (1) + c =
`(3)/(2)` + c ( subtract
`(3)/(2)` from both sides )

-
`(3)/(2)` = c

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