Question

Write the equation of a line that passes through the points (-2, -8) and (2, -6).

Answer 1

y =
`(1)/(2)` x - 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 ) = (- 2, - 8) and (x₂, y₂ ) = (2, - 6)

m =
`(-6+8)/(2+2)` =
`(2)/(4)` =
`(1)/(2)` , thus

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

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

Using (2, - 6), then

- 6 = 1 + c ⇒ c = - 6 - 1 = - 7

y =
`(1)/(2)` x - 7 ← equation of line