Question

How do you write an equation of a line through points (3,1) and (4,-4)?

Answer 1

y = - 5x + 16

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 ) = (4, - 4 )

m =
`(-4-1)/(4-3)` =
`(-5)/(1)` = - 5 , then

y = - 5x + c ← is the partial equation

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

using (3, 1 )

1 = - 5(3) + c = - 15 + c ( add 15 to both sides )

16 = c

y = - 5x + 16 ← equation of line