I need help with this problem

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  (d)  y = -2x +8

Step-by-step explanation:

The parallel line will have the same x-coefficient, eliminating choices B and C. If it goes through point (4, 0), then (x, y) = (4, 0) will satisfy the equation.

  A: 0 = -2(4) +4 = -4 . . . . . not true

  D: 0 = -2(4) +8 . . . . . . . . true

The equation you're looking for is ...

  y = -2x +8

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Additional comment

Since you know the slope is -2 and a point on the line is (4, 0), you can use the point-slope form of the equation for a line as a starting point.

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

For m = -2, and (h, k) = (4, 0), the equation becomes ...

  y -0 = -2(x -4)

Simplified to slope-intercept form, this is ...

  y = -2x +8