Question

Find the equation of the straight line passing through each of the following pairs of points.

(16 , 13) and (4, -5)

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 ) = (16, 13 ) and (x₂, y₂ ) = (4, - 5 )

m =
`(-5-13)/(4-16)` =
`(-18)/(-12)` =
`(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 (12, 13 ) , then

13 = 24 + c ⇒ c = 13 - 24 = - 11

y =
`(3)/(2)` x - 11 ← equation of line