Question

Find the equation of a line that passes through the points (6,4) and (8,2).

Leave your answer in the form
y
=
m
x
+
c

Answer 1

y = - x + 10

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 ) = (6, 4 ) and (x₂, y₂ ) = (8, 2 )

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

y = - x + c ← is the partial equation

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

using (6, 4 ) , then

4 = - 6 + c ⇒ c = 4 + 6 = 10

y = - x + 10 ← equation of line