Answer:
First of all let's write the slope-intercept form of the equation of a line, which is:
[tex]y=mx+b \\ \\ Where: \\ \\ m: \ slope \\ \\ b: \ y-intercept[/tex]
So we just need to find [tex]m \ and \ b[/tex] to solve this problem.
Moreover, this problem tells us that Amir drove from Jerusalem down to the lowest place on Earth, the Dead Sea, descending at a rate of 12 meters per minute. So this rate is the slope of the line, that is:
[tex]m=-12[/tex]
Negative slope because Amir is descending. So:
[tex]y=-12x+b[/tex]
To find [tex]b[/tex], we need to use the information that tells us that he was at sea level after 30 minutes of driving, so this can be written as the point [tex](30,0)[/tex]. Therefore, substituting this point into our equation:
[tex]y=-12x+b \\ \\ 0=-12(30)+b \\ \\ 0=-360+b \\ \\ \therefore b=360[/tex]
Finally, the equation of Amir's altitude relative to sea level (in meters) and time (in minutes) is:
[tex]\boxed{y=-12x+360}[/tex]
Whose graph is shown bellow.
