In a lab experiment 8 grams of acid were produced in 28 minutes and 17 grams in 47 minutes. Let g be the number of grams and m be the number of minutes. Find a linear equation that you could use to calculate g for any number of minutes
we have two points, so the equation for the line is
(g-8) = (17-8)/(47-28) (m-28)
156g
To find a linear equation that can be used to calculate the number of grams produced for any number of minutes, we first need to find the slope of the line.
The slope of a line is calculated using the formula:
slope = (change in y) / (change in x)
In this case, the "change in y" represents the change in the number of grams (g), and the "change in x" represents the change in the number of minutes (m).
Using the given data points, we can calculate the slope:
slope = (17 g - 8 g) / (47 min - 28 min)
= 9 g / 19 min
Now, we have the slope of the line. To find the equation of the line, we also need to determine the y-intercept (b).
To find the y-intercept, we can use one of the data points (8 grams produced in 28 minutes) and substitute it into the equation y = mx + b, where y represents the number of grams (g) and x represents the number of minutes (m).
8 g = (9 g / 19 min) * 28 min + b
Simplifying the equation:
8 g = (252 g/min) + b
8 g - (252 g/min) = b
b = 8 g - (252 g/min)
Therefore, the equation that can be used to calculate the number of grams (g) for any number of minutes (m) is:
g = (9 g / 19 min) * m + (8 g - (252 g/min))
Simplifying further:
g = (9/19) * m + (8 - 252/19) g
g = (9/19) * m + (152/19) g
So, the linear equation that can be used to calculate g for any number of minutes is:
g = (9/19) * m + (152/19)