Question

while playing outside in the snow, janet built a mini snowman on a cookie sheet to show her parents. after janet brought the snowman inside, it got shorter as it melted. this situation can be modeled as a linear relationship. chart: snowmans height (inches) vs time inside (hours), line starting at (0,18) and decreasing what does the slope of the line tell you about the situation?

Explanation:

Step1: Identify two points

From the graph, when \( x = 0 \) (time = 0 hours), \( y = 18 \) inches (initial height). When \( x = 4 \) hours, \( y = 8 \) inches.

Step2: Calculate the slope

The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Substituting \( (x_1,y_1)=(0,18) \) and \( (x_2,y_2)=(4,8) \), we get \( m=\frac{8 - 18}{4 - 0}=\frac{- 10}{4}=-2.5 \).

Step3: Interpret the slope

The slope is - 2.5 inches per hour. This means the snowman's height decreases by 2.5 inches for each hour it is inside (as time \( x \) increases by 1 hour, height \( y \) decreases by 2.5 inches due to melting).

Answer:

The slope of -2.5 inches per hour tells us that the snowman's height decreases by 2.5 inches for each hour it is inside (it melts at a rate of 2.5 inches per hour).