Question

What is the equation of a line that passes
through the points (-3, 7) and (9, -1)?

Answer 1

y = -
`(2)/(3)` + 5

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 ) = (- 3, 7 ) and (x₂, y₂ ) = (9, - 1 )

substitute these values into the formula for m

m =
`(-1-7)/(9-(-3))` =
`(-8)/(9+3)` =
`(-8)/(12)` = -
`(2)/(3)` , then

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

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

using (- 3, 7 ) for x and y in the partial equation

7 = -
`(2)/(3)` (- 3) + c = 2 + c ( subtract 2 from both sides )

5 = c

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