Question

melinda works at a cafe. each day that she works, she records x, the total dollar amount of her customers bills and then y, her total daily wages. the table shows her data for 2 weeks. according to the line of best fit, what is the minimum amount, to the nearest dollar, melinda will earn for each day of work, even if she serves no customers? $18 $26 $36 $40

Explanation:

Step1: Understand the linear regression equation

The linear regression equation is \(y = 0.177x+26.936\), where \(y\) is the total daily wages and \(x\) is the total dollar amount of customers' bills.

Step2: Substitute \(x = 0\) (no customers) into the equation

When \(x = 0\), we have \(y=0.177\times0 + 26.936\).
Since \(0.177\times0=0\), then \(y = 26.936\).

Step3: Round to the nearest dollar

Rounding \(26.936\) to the nearest dollar. Using the rounding rule (if the decimal part is \(0.5\) or more, round up; if less than \(0.5\), round down). Here, \(26.936\approx27\). But looking at the options, we can also note that in the context of the line - of - best - fit graph (visual inspection of the y - intercept of the line \(y = 0.177x + 26.936\), when \(x = 0\), the value of \(y\) is approximately \(26.936\) which is closest to \(26\) among the given options (assuming a possible mis - calculation in the problem's option setup based on the equation \(y=mx + b\) where \(b\) is the y - intercept and \(b = 26.936\)).

Answer:

\(\$26\)