Question

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

2 x + 3y - 5 = 0
-2 x+3y-5= 0
2 x-3 y-5= 0

Answer 1

A

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, - 1) and (x₂, y₂ ) = (- 2, 3)

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

y = -
`(2)/(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 =
`(4)/(3)` + c ⇒ c = 3 -
`(4)/(3)` =
`(5)/(3)`

y = -
`(2)/(3)` x +
`(5)/(3)` ← in slope- intercept form

Multiply through by 3 to clear the fractions

3y = - 2x + 5 ( add 2x to both sides )

2x + 3y = 5 ( subtract 5 from both sides )

2x + 3y - 5 = 0 ← in general form