Question

How to find the equation of this line?

Answer 1

y = -
`(6)/(7)` x -
`(10)/(7)`

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, 2 ) and (x₂, y₂ ) = (3, - 4) ← 2 points on the line

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

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

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

Using (- 4, 2 ), then

2 =
`(24)/(7)` + c ⇒ c = 2 -
`(24)/(7)` = -
`(10)/(7)`

y = -
`(6)/(7)` x -
`(10)/(7)` ← equation of line