Which equation represents a line parallel to the graph of2x − 4y = 16?(1) y=1/2x - 5 (2) y=-1/2x + 4 (3) y= -2x + 6 (4) y= 2x + 8

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The equation of the line 2x − 4y = 16 can be written as

2x − 4y = 16

=> -4y = -2x + 16

=> y = x/2 + 4

This is in the form y = mx + c, where m is the slope of the line. A line parallel to the given line should have a slope of (1/2)

Of the options provided:

1. y = (1/2)x - 5 has a slope (1/2)
2. y = (-1/2)x + 4 has a slope (-1/2)
3. y = -2x + 6 has a slope -2
4. y = 2x + 8 has a slope 2

Only option 1 or y = (1/2)x - 5 is parallel to the given line.

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The equation to a line parrallel to any other line will have the same slope as that line

ie all parallel lines will have the same slopes

your equation is 2x -4y =16

rearranging the terms, we have -4y = -2x + 16

dividing the equation by -4 to make the coefficient of y as 1 we have

y= -2/-4 x + 16/-4

ie y=1/2 x - 4

Note that the  slope of the line y = mx + c is m

so the slope of the given line  is 1/2

from the given options there is only one line with slope 1/2 which if option 1