Answer: d) y = 8x
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Explanation:
To find the rate of change, we'll need to find the slope.
Focus on Marisol's data table. Let's pick the first two rows to see that
(x1,y1) = (2,12)
(x2,y2) = (3,18)
The slope through these points is....
m = (y2-y1)/(x2-x1)
m = (18-12)/(3-2)
m = 6/1
m = 6
So she can purify 6 ounces of water per hour. We'll keep this rate in mind for later.
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Now move onto Timothy's table
Again we'll pick the first two rows. You can pick any two rows you want, but the first two just seems most convenient.
(x1,y1) = (4,36)
(x2,y2) = (6,54)
m = (y2-y1)/(x2-x1)
m = (54-36)/(6-4)
m = 18/2
m = 9
Timothy's machine can purify at a rate of 9 ounces per hour. His rate is faster compared to Marisol.
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To summarize, we have these rates
- Marisol's rate = 6 oz per hr
- Timothy's rate = 9 oz per hr
Zorian's rate must be between 6 and 9 oz per hour.
So we must look through the answer choices and see which slope is between 6 and 9. That would be for the equation y = 8x since the slope here is 8, which is between 6 and 9.
Something like y = 15x doesn't work because the rate 15 is larger than Timothy's rate.
So that's why y = 8x is the answer.
Side note: The equation y = 8x is the same as y = 8x+0. It is in the form y = mx+b with slope m = 8 and y intercept b = 0.
