Question

write an equation in slope intercept form for the line that passes through the points (3,2) and(-9,6)

Answer 1

y = -
`(1)/(3)` x + 3

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 = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (3, 2) and (x₂, y₂ ) = (- 9, 6)

m =
`(6-2)/(-9-3)` =
`(4)/(-12)` = -
`(1)/(3)`, hence

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

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

Using (- 9, 6), then

6 = 3 + c ⇒ c = 6 - 3 = 3

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