Question

Find the equation of a line that goes through the points (8, -9) and (-4, 15).

Answer 1

y = - 2x + 7

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 ) = (8, - 9) and (x₂, y₂ ) = (- 4, 15)

m =
`(15+9)/(-4-8)` =
`(24)/(-12)` = - 2, thus

y = - 2x + c ← is the partial equation

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

Using (8, - 9), then

- 9 = - 16 + c ⇒ c = - 9 + 16 = 7

y = - 2x + 7 ← equation of line