Question

On a coordinate plane, a line goes through (negative 4, 0) and (4, negative 4). A point is at (2, 3).

Answer 1

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Answer:

  (b)  x +2y = 8

Step-by-step explanation:

The only offered line that includes the given point is ...

  x +2y = 8

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We can check the other choices:

  x + 2y = 2 +2(3) = 2+6 = 8 . . . matches B (not A)

  2x +y = 2(2) +3 = 4+3 = 7 . . . . not a choice

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Getting there from scratch

The standard form equation for a line can be written from ...

  (y2 -y1)x -(x2 -x1)y = constant

  (-4 -0)x -(4 -(-4))y = constant . . . . using the given points (-4, 0) and (4, -4)

  -4x -8y = constant

For standard form, we need the leading coefficient to be positive, and we need common factors removed. We can get there by dividing by -4.

  x +2y = constant

The value of the constant will be whatever it takes for the given point to lie on the line. For (x, y) = (2, 3) to be a solution, we must have ...

 x +2y = (2) +2(3) = constant = 8

The desired line has the equation ...

  x +2y = 8

Answer 2

Answer:

B on edge

Step-by-step explanation: