Question

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

y=2x-2
y=-2x-4
y=-2x-2
y= 2x+4

Answer 1

y = - 2x - 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 = (- 2, 2) and (x₂, y₂ ) = (1, - 4)

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

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

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

Using (- 2, 2), then

2 = 4 + c ⇒ c = 2 - 4 = - 2

y = - 2x - 2 ← equation of line