Question

Find the equation for the line below.

Answer 1

y =
`(3)/(4)` x -
`(1)/(2)`

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 ) = (- 6, - 5) and (x₂, y₂ ) = (2, 1) ← 2 points on the line

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

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

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

Using (2, 1 ) , then

1 =
`(3)/(2)` + c ⇒ c = 1 -
`(3)/(2)` =
`(2)/(2)` -
`(3)/(2)` = -
`(1)/(2)`

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