Answer: -0.95V+590
The full equation is M = -0.95V+590 but the "M=" portion isn't typed in the box.
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Explanation:
For now, I'll use x in place of V and y in place of M
- x = V = amount of oil used up (in mL)
- y = M = the weight of the bottle (in grams)
If Sophia uses x = 0 mL of oil, then the bottle weighs y = 590 grams since that's the starting amount. This leads to the ordered pair (x,y) = (0,590).
If she uses x = 200 mL of oil, then the weight is now y = 400 grams. We have another point (200,400)
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Let's compute the slope through the points (0,590) and (200,400)
m = (y2-y1)/(x2-x1)
m = (400-590)/(200-0)
m = -190/200
m = -0.95
The slope is -0.95
The y intercept is 590 because this is the starting amount
We go from y = mx+b to y = -0.95x+590
Then we'll replace x with V and y with M to get M = -0.95V+590
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Let's see what happens if she uses V = 200 mL
M = -0.95V + 590
M = -0.95*200+590
M = -190+590
M = 400
That helps confirm the answer.
The portion -0.95*200 = -190 represents Sophia using 190 grams of oil (ie 590-400 = 190).
