Question

catering events
the equation for the line of best fit is ( y = 25x + 200 ). according to the equation, which of these statements is true?
each additional guest increases the total cost of catering an event by about $200.
each additional guest increases the total cost of catering an event by about $25.

Explanation:

Step1: Recall the slope - intercept form of a linear equation

The slope - intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. In the given equation \(y=25x + 200\), \(x\) represents the number of guests and \(y\) represents the total cost.

Step2: Interpret the slope

The slope \(m = 25\). In the context of the problem, the slope represents the rate of change of the total cost (\(y\)) with respect to the number of guests (\(x\)). Mathematically, if we consider two points \((x_1,y_1)\) and \((x_2,y_2)\) on the line, \(m=\frac{y_2 - y_1}{x_2 - x_1}\). When \(x_2=x_1 + 1\) (i.e., when we add one more guest), \(y_2-y_1=m(x_2 - x_1)\). Substituting \(x_2 - x_1 = 1\) into the formula \(y_2 - y_1=m\times1\). Since \(m = 25\), when the number of guests (\(x\)) increases by 1, the total cost (\(y\)) increases by 25.

Answer:

Each additional guest increases the total cost of catering an event by about \(\$25\).