Question

write the equation of the line in either form (slope intercept or point slope form) that contains points (4,-5) (8,1)

Answer 1

y =
`(3)/(2)` x - 11

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, - 5 ) and (x₂, y₂ ) = (8, 1 )

m =
`(1-(-5))/(8-4)` =
`(1+5)/(4)` =
`(6)/(4)` =
`(3)/(2)` , then

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

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

Using (8, 1 ) , then

1 = 12 + c ⇒ c = 1 - 12 = - 11

y =
`(3)/(2)` x - 11 ← equation of line in slope- intercept form