Answer: Choice C. y = (-1/2)x+7
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Step-by-step 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.
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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