Question

elijah started hiking at an elevation of -12 feet below sea level. he hiked up at a rate of 9 feet per minute. this graph represents the relationship between the number of minutes and his elevation. use the slope and vertical intercept to write an equation. this graph represents the situation. what is the slope of the line? slope = \boxed{}

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
We can use the y - intercept \((0, - 12)\) and another point, say \((1, - 3)\) (from the graph).

Step2: Calculate the slope

Substitute \( x_1 = 0,y_1=-12,x_2 = 1,y_2=-3 \) into the slope formula:
\( m=\frac{-3-(-12)}{1 - 0}=\frac{-3 + 12}{1}=\frac{9}{1}=9 \)
Or, we know from the problem that the rate of hiking up is 9 feet per minute. In the context of a linear equation \( y=mx + b \) (where \( y \) is elevation, \( x \) is time), the rate of change (slope) is equal to the speed of hiking. Since he is hiking up at 9 feet per minute, the slope \( m = 9 \).

Answer:

9