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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

User Shaneb
by
8.3k points

2 Answers

5 votes

Answer:

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

User Chris Harcourt
by
7.8k points
4 votes

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
User David Hammond
by
8.4k points

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