Pls help it due today

 Choice C.  y = (-1/2)x+7

Explanation:

The slope of the graphed line is -1/2 because we drop down 1 unit on the y axis each time we move to the right 2 units along the x axis. We could apply the slope formula for any two points on the diagonal line to also get a slope of -1/2.

The slope formula is m = (y2-y1)/(x2-x1).

Any two parallel lines have the same slope, but different y intercepts. So the parallel line will also have slope -1/2. Right away we can see the answer must be choice C. This is the only equation with slope -1/2 of the choices given.

Recall that slope intercept form y = mx+b has m as the slope. Not to be confused with the label m of the graphed line.

Note how plugging x = 6 into the equation for choice C leads to...

y = (-1/2)*x + 7

y = (-1/2)*6 + 7

y = -3 + 7

y = 4

Showing that (x,y) = (6,4) is on the equation y = (-1/2)x + 7. This confirms the answer.

Let's say we didn't have multiple choice answers to pick from, and instead it was fill in the blank. To find the y intercept b, we can do the following

y = mx+b

y = (-1/2)x + b ... plug in given slope m = -1/2

4 = (-1/2)*6 + b plug in the given point (x,y) = (6,4)

4 = -3 + b

4+3 = -3+b+3 ... adding 3 to both sides

7 = b

b = 7

Knowing that m = -1/2 and b = 7, we can update y = mx+b into y = (-1/2)x+7

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