Question

Given the two points (1,4 ) and (-4, -5) how do I find m and b using slope intercept form?

Answer 1

m =
`(9)/(5)` , b =
`(11)/(5)`

Explanation:

the equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b 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 ) = (- 4, - 5 )

m =
`(-5-4)/(-4-1)` =
`(-9)/(-5)` =
`(9)/(5)` , then

y =
`(9)/(5)` x + b ← is the partial equation

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

using (1, 4 )

4 =
`(9)/(5)` (1) + b =
`(9)/(5)` + b ( subtract
`(9)/(5)` from both sides )

4 -
`(9)/(5)` = b

`(20)/(5)` -
`(9)/(5)` = b , that is

b =
`(11)/(5)`

y =
`(9)/(5)` x +
`(11)/(5)` ← equation of line in slope- intercept form

with slope m =
`(9)/(5)` and y- intercept b =
`(11)/(5)`