Question

A line includes the points (-8,8) and (6,4). Select the correct point slope form equations of this line. (Remember there can be more than one)

Group of answer choices

y-8=(-2/7)(x+8)

y+8=(-2/7)(x-8)

y-4=(-2/7)(x-6)

Answer 1

first and third options

Explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Calculate m using the slope- formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

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

m =
`(4-8)/(6+8)` =
`(-4)/(14)` = -
`(2)/(7)`

using (a, b ) = (- 8, 8 ), then

y - 8 = -
`(2)/(7)` (x - (- 8) ) , that is

y - 8 = -
`(2)/(7)`(x + 8) ← first option

using (a, b ) = (6, 4 ), then

y - 4 = -
`(2)/(7)` (x - 6) ← third option

Answer 2

y-8=(-2/7)(x+8) and y-4=(-2/7)(x-6)

Explanation:

Point slope form equation: y - y₁ = m(x - x₁)

m is the same for all your answer choices, so you can disregard that part.

First point: (-8,8)

x₁ = -8; y₁ = 8

Plug those values into the point slope form equation and you get:

y-8=(-2/7)(x+8)

Do the same for the second point, and you get:

y-4=(-2/7)(x-6)