Question

Write a linear equation that goes through the points (-1,-10) and (5,2).

Answer 1

y = 2x - 8

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 ) = (- 1, - 10) and (x₂, y₂ ) = (5, 2)

m =
`(2-(-10))/(5-(-1))` =
`(2+10)/(5+1)` =
`(12)/(6)` = 2 , then

y = 2x + c ← is the partial equation

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

Using (5, 2 ) , then

2 = 10 + c ⇒ c = 2 - 10 = - 8

y = 2x - 8 ← equation of line