Question

hilary measured the depth of the snow in her front yard for 7 days. an equation for the line of best fit for hilary’s data is ( y = -0.5x + 8 ). let ( x ) represent the number of days. let ( y ) represent the depth of the snow in inches. which statement best describes the meaning of the slope in this equation?

• the depth of the snow decreased 0.5 inch per day.
• the depth of the snow increased 0.5 inch per day.
• the depth of the snow decreased 8 inches per day.
• the depth of the snow increased 8 inches per day.

Explanation:

Step1: Recall slope-intercept form

The slope - intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. In the given equation \(y=- 0.5x + 8\), the slope \(m=-0.5\).

Step2: Interpret the slope

The slope \(m\) represents the rate of change of \(y\) with respect to \(x\). Here, \(x\) is the number of days and \(y\) is the depth of the snow. A negative slope means that as \(x\) (number of days) increases, \(y\) (depth of snow) decreases. The value of the slope is \(- 0.5\), which means that for each increase of 1 in \(x\) (each day), \(y\) (snow depth) decreases by 0.5. So the depth of the snow decreases 0.5 inch per day.

Answer:

The depth of the snow decreased 0.5 inch per day. (The option corresponding to this statement, e.g., if it's the first option among the four, then "A. The depth of the snow decreased 0.5 inch per day" depending on the original option numbering. From the given options, the correct one is "The depth of the snow decreased 0.5 inch per day".)