Question

Amir drove from Jerusalem down to the lowest place on earth the Dead Sea descending at a rate of 12 meters per minute. He was at sea level after 30 minutes of driving. Graph Amir’s altitude relative to sea level (in meters) as a function of time (in minutes).

Answer 1

Define the axis:

Let the y-axis be the altitude

The x-axis be be function of time

Identify 2 coordinates on the graph:

Rate = 12m/min

⇒ When x = 1, y = 12

He is at sea level after 30 mins

⇒ When x = 30, y = 0

Now that we have the two coordinates, we can form the equation:

Coordinates = (1, 12) and (30,0)

Format of a linear equation: y = mx + c

Find the slope:

slope = (y2 - y1) / (x2 - x1) = (0 - 12)/(30 - 12) = -12/18 = -2/3

Equation: y = -2/3 x + c

Find the y-intercept:

At point (30, 0),

0 = -2/3 (30) + c

c = 20

Equation of the graph = -2/3 x + 20

Now that we have all the information we need to plot the graph. (See Attached for the graph plotted)