Question

the equation for the line of best fit is y = -8.12x + 43.4. according to the equation, which of these statements is true? students typically started the school year with about $43 in their accounts. students tend to spend between $8 and $9 each day.

Explanation:

Step1: Analyze the y - intercept

The equation of the line is \(y=-8.12x + 43.4\). In the linear equation \(y = mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept), when \(x = 0\) (at the start of the school year, i.e., \(0\) weeks since school started), \(y=b\). Substituting \(x = 0\) into \(y=-8.12x + 43.4\), we get \(y=43.4\approx43\). This means the initial balance (when \(x = 0\)) is about \(\$43\).

Step2: Analyze the slope

The slope \(m=-8.12\). The slope represents the rate of change of \(y\) with respect to \(x\). Here, \(x\) is in weeks. The slope \(m=-8.12\) means the balance decreases by approximately \(\$8.12\) per week (not per day).

Answer:

Students typically started the school year with about \(\$43\) in their accounts.