Linear Modeling
We are given the mathematical model represented by:
n = 456 - 3T
Where n is the number of hot chocolate sold per day in a coffee shop and T is the average daily temperature in °F.
The slope-intercept form of a line is:
n = mT + b
Where m is the slope of the graph of the line and b is the y-intercept.
Comparing this equation with the given model, we have m=-3 and b=456.
A negative slope means that the dependent variable (n) decreases when the independent variable (T) increases.
This can also be said like: The dependent variable (n) increases when the independent variable (T) decreases.
The correct answer is D. But let's prove it
Set the temperature at T=20°F
The number of cups is calculated below:
n = 456 - 3*20 = 396
Now decrease the temperature to T=19°F
n = 456 - 3*19 = 399
Note we have decreased the temperature by 1°F and the number of cups has increased by 3. Answer: D