Question

Determine the slop, m, and y-intercept,b,of a line that passes through the points (2,4) and (-4,1)

Answer 1

slope m =
`(1)/(2)` , y- intercept b = 3

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) )`

let (x₁, y₁ ) = (2, 4 ) and (x₂, y₂ ) = (- 4, 1 )

substitute these values into the formula for m

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

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

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

using (2, 4 ) for x and y in the partial equation

4 =
`(1)/(2)` (2) + b = 1 + b ( subtract 1 from both sides )

3 = b

y =
`(1)/(2)` x + 3 ← in slope- intercept form

with slope m =
`(1)/(2)` and y- intercept b = 3