Question

What is the equation of the line that passes through the points (- 2, 3) and (4, 1)

Answer 1

y = -
`(1)/(3)` x +
`(7)/(3)`

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, 3) and (x₂, y₂ ) = (4, 1)

m =
`(1-3)/(4+2)` =
`(-2)/(6)` = -
`(1)/(3)` , thus

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

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

Using (- 2, 3), then

3 =
`(2)/(3)` + c ⇒ c = 3 -
`(2)/(3)` =
`(7)/(3)`

y = -
`(1)/(3)` x +
`(7)/(3)` ← equation of line