Question

the line of best fit.
silver city lake
the equation for the line of best fit is ( y = -\frac{1}{2}x + 25 ). according to the equation, which of these statements is true?
the depth of the lake is expected to decrease about 1 foot every 2 months during the drought.
the depth of the lake is expected to decrease about 2 feet every 1 month during the drought.

Explanation:

Step1: Analyze the slope - intercept form

The equation of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. In the given equation \(y=-\frac{1}{2}x + 25\), \(m =-\frac{1}{2}\). The slope \(m=\frac{\Delta y}{\Delta x}\), where \(\Delta y\) is the change in \(y\) (depth) and \(\Delta x\) is the change in \(x\) (month).

Step2: Interpret the slope

Since \(m =-\frac{1}{2}=\frac{\text{Change in depth}}{\text{Change in month}}\), when \(\Delta x = 2\) (change in month), \(\Delta y=- 1\). This means that for a change of \(2\) months (\(\Delta x = 2\)), the depth (\(y\)) changes by \(-1\) (a decrease of \(1\) foot).

Answer:

The depth of the lake is expected to decrease about 1 foot every 2 months during the drought.