Question

What is an equation of the line that passes through the points (2,−2) and (3,−4)?

Answer 1

Steps to finding the line that passes through two points as given:

1) Find the slope:

`Slope = (y_(2)-y_(1) )/(x_(2)-x_(1))`

• 
  `(x_(1),y_(1))=(2,-2)`
• 
  `(x_(2),y_(2))=(3,-4)`

`Slope = (-4--2)/(3-2) =(-2)/(1) =-2`

2) Use the point-slope form to form the basic equation:

Point-slope form -->
`(y-y_(0))=m(x-x_(0))`

• 
  `(x_(0),y_(0)) = (2,-2)` <-- could be any point on the line
• 
  `m = -2`

`(y + 2) = -2(x-2)\\y + 2 = -2x + 4\\y = -2x + 2`

Hope that helps!