Question

Write an equation for a line that passes through (-4, 5) and (8, 2). Make sure to simplify your slope.

Answer 1

y = -
`(1)/(4)` x + 4

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate the slope m, using the slope formula

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

let (x₁, y₁ ) = (- 4, 5) and (x₂, y₂ ) = (8, 2) ← the 2 points the line passes through

substitute these values into the formula for m

m =
`(2-5)/(8-(-4))` =
`(-3)/(8+4)` =
`(-3)/(12)` = -
`(1)/(4)` , then

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

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

using (- 4, 5 ) for x and y in the partial equation

5 = -
`(1)/(4)` (- 4) + c = 1 + c ( subtract 1 from both sides )

4 = c

y = -
`(1)/(4)` x + 4 ← equation of line