Question

What is an equation of the line that passes through the points (4, -5) and (2, 0)?

Answer 1

y = -
`(5)/(2)` x + 5

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 ) = (2, 0)

m =
`(0+5)/(2-4)` =
`(5)/(-2)` = -
`(5)/(2)` , then

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

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

Using (2, 0 )

0 = - 5 + c ⇒ c = 0 + 5 = 5

y = -
`(5)/(2)` x + 5 ← equation of line