SOLUTION: In a lab experiment 4 grams of acid were produced in 10 minutes and 15 grams in 50 minutes. Let y be the grams produced in x minutes. Write an equation for grams produced.

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Question 205132: In a lab experiment 4 grams of acid were produced in 10 minutes and 15 grams in 50 minutes. Let y be the grams produced in x minutes. Write an equation for grams produced.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
In a lab experiment 4 grams of acid were produced in 10 minutes and 15 grams in 50 minutes. Let y be the grams produced in x minutes. Write an equation for grams produced.

When x = 10 minutes, then y = 4 grams.  
When x = 50 minutes, then y = 15 grams.

This information can be interpreted as two points on a line.
So the problem is the same as:

Find the equation of the line passing through the points (10,4) and (50,15)

We use the slope formula:

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29=%2815-4%29%2F%2850-10%29=11%2F40

We use the point-slope formula:

y-y%5B1%5D=m%28x-x%5B1%5D%29

Substituting:

y-4=%2811%2F40%29%28x-10%29

Multiply through by 40

40%2Ay-40%2A4=40%2A%2811%2F40%29%28x-10%29

40%2Ay-40%2A4=cross%2840%29%2A%2811%2Fcross%2840%29%29%28x-10%29

40y-160=11%28x-10%29

40y-160=11x-110

Add 160 to both sides:

40y=11x%2B50

Divide through by 40

40y%2F40=11x%2F40%2B50%2F40

y=%2811%2F40%29x%2B5%2F4

Or you could make the fractions into decimals:

y=0.275x%2B1.25

Edwin