How many of the equations listed below represent the line passing through the points (1,4) and (5, -4) 2x+y=6
Y=2x+6
Y-4=-2(x-1)
Y+4=-2(x-1)

  2

Step-by-step explanation:

The slope of the line through the given points is found using the formula ...

  m = (y2 -y1)/(x2 -x1)

  m = (-4 -4)/(5 -1) = -8/4 = -2

The equations are written in standard form, slope-intercept form, and point-slope form. We can eliminate equations with slope that is not -2. That removes choice B.

The point-slope equation form is ...

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

Using the given points, the equations would be ...

  y -4 = -2(x -1) . . . . matches C

  y +4 = -2(x -5) . . . . differs from D, so D can be eliminated

Rearranging the point-slope form to standard form, we find ...

  y = -2x +2 +4

  2x +y = 6 . . . . matches A

So, equations A and C represent the line through the given points. Two of the equations represent the line.

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