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.
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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=(y[2]-y[1])/(x[2]-x[1])=(15-4)/(50-10)=11/40}}}

We use the point-slope formula:

{{{y-y[1]=m(x-x[1])}}}

Substituting:

{{{y-4=(11/40)(x-10)}}}

Multiply through by 40

{{{40*y-40*4=40*(11/40)(x-10)}}}

{{{40*y-40*4=cross(40)*(11/cross(40))(x-10)}}}

{{{40y-160=11(x-10)}}}

{{{40y-160=11x-110}}}

Add 160 to both sides:

{{{40y=11x+50}}}

Divide through by 40

{{{40y/40=11x/40+50/40}}}

{{{y=(11/40)x+5/4}}}

Or you could make the fractions into decimals:

{{{y=0.275x+1.25}}}

Edwin</pre>