Question

Write an equation of a line in slope-intercept form using the given information.

passes through (3,1) and (9,3)

Answer 1

y =
`(1)/(3)` x

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 ) = (3, 1 ) and (x₂, y₂ ) = (9, 3 )

m =
`(3-1)/(9-3)` =
`(2)/(6)` =
`(1)/(3)` , then

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

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

using (3, 1 )

1 =
`(1)/(3)` (3) + c = 1 + c ( subtract 1 from both sides )

0 = c

then

y =
`(1)/(3)` x ← equation of line