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
treat it as having 2 ordered pairs
(28, 8) and (47,17) in the form (m,g)
slope = (17-8)/(47-28) = 9/19
using (28,8)
g-8 = (9/19)(m-28)
19g - 152 =9m - 252
9m - 19g = 100
or
-19g = -9m + 100
g =(9/19)m - 100/19
To calculate the linear equation for the relationship between the number of grams (g) and the number of minutes (m), we can use the formula for the equation of a straight line: y = mx + b, where y represents the dependent variable (in this case, the number of grams) and x represents the independent variable (the number of minutes).
Let's use the two data points given:
Data Point 1: (28 minutes, 8 grams)
Data Point 2: (47 minutes, 17 grams)
We can use these data points to find the slope (m) and the y-intercept (b) of the equation.
First, calculate the slope (m):
m = (change in y) / (change in x)
m = (17 grams - 8 grams) / (47 minutes - 28 minutes)
m = 9 grams / 19 minutes
Next, substitute one of the data points (let's use Data Point 1, 28 minutes and 8 grams) into the equation to solve for b:
8 grams = (9 grams / 19 minutes) * 28 minutes + b
8 grams = (252 grams / 19 minutes) + b
8 grams = (13.26 grams/minute) + b
Rewrite the equation:
b = 8 grams - (13.26 grams/minute)
b ≈ 6.74 grams/minute
Therefore, the linear equation that relates the number of grams (g) to the number of minutes (m) is:
g = (9 grams / 19 minutes) * m + 6.74 grams
This equation can be used to calculate the number of grams (g) for any given number of minutes (m).
To find a linear equation that relates the number of grams (g) to the number of minutes (m) in this lab experiment, we can use the concept of the rate of acid production.
The rate of acid production can be calculated by dividing the change in grams by the change in minutes. In this case, the change in grams is 17 grams - 8 grams = 9 grams, and the change in minutes is 47 minutes - 28 minutes = 19 minutes.
Therefore, the rate of acid production is 9 grams / 19 minutes.
Now, we have the rate of acid production, but we still need to find the initial amount of acid when the experiment started, which is the y-intercept (b) in our linear equation.
Let's use the first data point, where 8 grams were produced in 28 minutes. We can substitute g = 8 grams and m = 28 minutes into the equation and solve for b:
g = rate * m + b
8 grams = (9 grams / 19 minutes) * 28 minutes + b
After simplifying:
8 grams = (9/19) * 28 minutes + b
To solve for b, we subtract (9/19) * 28 from both sides:
b = 8 grams - (9/19) * 28 minutes
Now we have the y-intercept (b) value, we can write the linear equation:
g = (9 grams / 19 minutes) * m + (8 grams - (9/19) * 28 minutes)
Simplifying further:
g = (9/19) * m + (8 - (9/19) * 28)
This is the linear equation that relates the number of grams (g) to the number of minutes (m) in the lab experiment.