Question

What is an equation of the line that passes through the points (-4, 8) and (6, 3)?

Answer 1

y = -
`(1)/(2)` x + 6

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 ) = (- 4, 8 ) and (x₂, y₂ ) = (6, 3 )

m =
`(3-8)/(6-(-4))` =
`(-5)/(6+4)` =
`(-5)/(10)` = -
`(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 (- 4, 8 )

8 = -
`(1)/(2)` (- 4) + c = 2 + c ( subtract 2 from both sides )

6 = c

y = -
`(1)/(2)` x + 6 ← equation of line