Question

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

a.) 2 x + 3 y - 5 = 0
b.) -2 x + 3 y - 5 = 0
c.) 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)` =
`(3+1)/(-6)` =
`(4)/(-6)` = -
`(2)/(3)` , then

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 ( subtract - 2x + 5 from both sides )

2x + 3y - 5 = 0 ← in general form