When buying gasoline, you notice that 14 gallons of gasoline is approximately the same as 53 liters. Use this information to find a linear model that relates gallons to liters. Then use the model to find the number of liters in 25 gallons. Round your answer to the nearest tenth.
14 g = 53 L
1 g = (53/14) L
then
25 g = (53/14)(25) L
= appr 94.6 L
To find a linear model that relates gallons to liters, we can use the given data point: 14 gallons is approximately the same as 53 liters.
The formula for a linear model is generally represented as: y = mx + b, where y is the dependent variable (liters), x is the independent variable (gallons), m is the slope, and b is the y-intercept.
We can use the given data point (14 gallons, 53 liters) to find the slope (m) of the linear model. The slope of a line is the amount the dependent variable changes for a unit change in the independent variable.
We can calculate the slope (m) using the formula: m = (change in y) / (change in x)
In this case, the change in y is 53 liters, and the change in x is 14 gallons.
So, m = 53 liters / 14 gallons.
Simplifying the expression, we get approximately m = 3.79 liters/gallon.
Now, we need to find the y-intercept (b) for the linear model. The y-intercept represents the point where the line intersects the y-axis (when x = 0).
Since we know that 14 gallons is approximately the same as 53 liters, we can use this data point as (x, y).
So, 14 gallons = 53 liters.
Substituting this into the linear equation, we get: 53 = 3.79(14) + b.
Simplifying the expression, we find: b = 53 - (3.79)(14).
Evaluating this expression, we get approximately b = -9.06 liters.
Now we have the slope (m = 3.79) and the y-intercept (b = -9.06).
So, the linear model relating gallons to liters is: y = 3.79x - 9.06.
To find the number of liters in 25 gallons using this linear model, we substitute x = 25 into the equation:
y = 3.79(25) - 9.06.
Evaluating this expression, we find: y ≈ 94.19 liters.
Therefore, there are approximately 94.19 liters in 25 gallons.
To find a linear model that relates gallons to liters, we can use the given information that 14 gallons is approximately the same as 53 liters.
Step 1: Determine the conversion factor
To find the conversion factor, divide the number of liters by the number of gallons: 53 liters / 14 gallons.
Conversion factor = 53 L / 14 gal
Step 2: Simplify the conversion factor
To simplify the conversion factor, divide both the numerator and denominator by their greatest common divisor, which is 1 in this case.
Conversion factor = 53/14 L/gal
Step 3: Write the linear model
The linear model relating gallons to liters is:
liters = (53/14) * gallons
Step 4: Use the model to find the number of liters in 25 gallons
To find the number of liters in 25 gallons, substitute the value of gallons into the linear model:
liters = (53/14) * 25
liters = 201.79
Rounded to the nearest tenth, the number of liters in 25 gallons is approximately 201.8 liters.