Question

Choose the equation that represents a line that passes through points (−1, 2) and (3, 1).

4x − y = −6
x + 4y = 7
x − 4y = −9
4x + y = 2

Answer 1

x + 4y = 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 ) = (- 1, 2 ) and (x₂, y₂ ) = (3, 1 )

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

y = -
`(1)/(4)` x + c ← is the partial equation

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

using (- 1, 2 )

2 =
`(1)/(4)` + c ⇒ c = 2 -
`(1)/(4)` = 1
`(3)/(4)` =
`(7)/(4)`

y = -
`(1)/(4)`x +
`(7)/(4)` ← in slope- intercept form

multiply through by 4 to clear the fractions

4y = - x + 7 ( add x to both sides )

x + 4y = 7 ← equation in standard form

Answer 2

equation of line in two point form is needed here.

• (y - y1) = [ (y2 - y1)/(x2-x1) ] (x - x1)

• y - (2) = [ (1 - 2)/(3 - (-1)) ] (x - (-1))

• y - 2 = [ -1/4 ] (x + 1)

• y = -(x/4) -1/4 + 2

• y = -x/4 + 7/4

• 4y = -x + 7

• x + 4y = 7