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? data x y 50 36 100 43 75 30 80 40 90 42 140 50 150 60 95 43 125 46 160 50 165 55 linear regression y = 0.177x + 25.936; r = 0.92 -10 ≤ x ≤ 200 -6 ≤ y ≤ 66

Explanation:

Step1: Identify the linear - regression equation

The line of best fit is given by the equation $y = 0.177x+25.936$, where $y$ is the total daily wages and $x$ is the total dollar amount of customers' bills.

Step2: Determine the value of $y$ when $x = 0$

When Melinda serves no customers, $x = 0$. Substitute $x = 0$ into the equation $y=0.177x + 25.936$.
$y=0.177\times0+25.936$.
Since $0.177\times0 = 0$, then $y = 25.936$.

Step3: Round the result

Rounding $25.936$ to the nearest dollar gives $y\approx26$.

Answer:

$26$ dollars (corresponds to the second option)