Question

Which equation models the line that passes through points (4, 6) and (−4, 8)

Answer 1

y = -
`(1)/(4)` 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 )

To calculate m use the slope formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (4, 6) and (x₂, y₂ ) = (- 4, 8)

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

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

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

Using (- 4, 8 ), then

8 = 1 + c ⇒ c = 8 - 1 = 7

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