Question

silver city is experiencing severe drought conditions. as a result, the depth of silver city lake is changing. this scatter plot shows the data collected by a local scientist. it also shows the line of best fit. 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 2 feet every 1 month during the drought. the depth of the lake is expected to decrease about 1 foot every 2 months during the drought.

Explanation:

Step1: Analyze the slope - intercept form

The equation of the line is $y =-\frac{1}{2}x + 25$, where the slope $m =-\frac{1}{2}$. In the context of the problem, $x$ represents the month and $y$ represents the depth of the lake.

Step2: Interpret the slope

The slope $m =-\frac{1}{2}$ means that for every increase of 2 in the value of $x$ (2 months), the value of $y$ (depth of the lake) decreases by 1. So the depth of the lake is expected to decrease about 1 foot every 2 months during the drought.

Answer:

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