Question

A line passes through the points (2,-4) and (6,10). What is the equation of the line?

Answer 1

y =
`(7)/(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 ) = (2, - 4) and (x₂, y₂ ) = (6, 10)

m =
`(10+4)/(6-2)` =
`(14)/(4)` =
`(7)/(2)` , thus

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

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

Using (2, - 4) , then

- 4 = 7 + c ⇒ c = - 4 - 7 = - 11

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