Answer: Choice A) M = 0.25n + 100
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Explanation:
For now, I'll treat n as x, and M as y.
In other words,
- x = number of CDs
- y = total mass in kg
Let's select two points from this graph. I'll pick (200,150) and (400,200)
The slope of the line through those points is
m = (y2-y1)/(x2-x1)
m = (200-150)/(400-200)
m = 50/200
m = 0.25
Now we'll use the point (x,y) = (200,150) along with that slope value to find the y intercept b
y = mx+b
150 = 0.25*200+b
150 = 50+b
150-50 = b
100 = b
b = 100
You could also use (x,y) = (400,200) and you should get the same b value.
In fact, any other point from this graph works as well.
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Since m = 0.25 and b = 100, we go from y = mx+b to y = 0.25x+100
This then translates over to M = 0.25n + 100 which is choice A
To help verify this, let's say we plugged in n = 100
M = 0.25*n + 100
M = 0.25*100 + 100
M = 25 + 100
M = 125
Which is confirmed by what the graph shows. I'll let you check the other points as well.
