Question

Write the linear equation in slope-intercept form given the following:
(-3, 7) and (6, -8)

Answer 1

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

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

with (x₁, y₁ ) = (- 3, 7) and (x₂, y₂ ) = (6, - 8)

m =
`(-8-7)/(6+3)` =
`(-15)/(9)` = -
`(5)/(3)` , then

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

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

Using (6, - 8) , then

- 8 = - 10 + c ⇒ c = - 8 + 10 = 2

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