Question

What is an equation of the line that passes through the points (-2, 1) and (-8,4)?

Answer 1

y = -
`(1)/(2)` x

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, 1) and (x₂, y₂ ) = (- 8, 4)

m =
`(4-1)/(-8-(-2))` =
`(3)/(-8+2)` =
`(3)/(-6)` = -
`(1)/(2)` , then

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

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

Using (- 8, 4 ) , then

4 = 4 + c ⇒ c = 4 - 4 = 0

y = -
`(1)/(2)` x ← equation of line