Suppose a tsunami has traveled 250 miles in 45 minutes and then traveled 630 miles after 2 hour. State the coordinates as to where the tsunami started ?

Question

Question is about functions and graphs 

Answer 1

The coordinates to where the tsunami started is  (0, y).  Time (minutes) is in the x axis and distance (miles) is in the y axis.

 

We have two given points:

 

P₁(45, 250)  and  P₂(120, 630)

 

note that 1 hour is equal to 60 minutes.

 

 

We can use these points to find a linear function.  This function is in the form  y=mx+b.

 

Find the slope of the linear function using the two points.

 

slope = (630 - 250) / (120 - 45)

        = 380 / 75

        = 76/15

       

 

The linear function is

 

y = (76/15)x + b

 

 

Use one of the points and plug it into the function to find b.  Use P₁.

 

 

250 = (76/15)(45) + b

 

250 = 228 + b

 

22 = b

 

 

The function that defines how far the tsunami travels is

 

y = (76/15)x + 22

 

 

The coordinates where the tsunami started is  (0, 22).