It takes Lin 1 hour to drive 62 miles,2 hours to drive 130 miles,and 3 hours to drive 195 miles. Write an equation for the relationship.Tell what the variables represent
think of having 3 points:
(1, 62), (2, 130) and (3, 195)
slope between first two = (130-62)/(2-1) = 68
slope between last two = (195-130)/(3-2) = 65
So the function is not linear.
We could write a quadratic function, is that what you want?
distance = at^2 + bt +c
for (1,62) --> 62 = a + b + c **
for (2,130) --> 130 = 4a + 2b + c ***
for (3,195) --> 195 = 9a + 3b + c ****
subtract ** from *** : 68 = 3a + b
subtract ** from ***: 65 = 5a + b
now subtract these last two:
-3 = 2a
a = -3/2
in 68 = 3a+b
68 = -9/2 + b
b = 145/2
now back in a+b+c = 62
-3/2 + 145/2 + c = 62
c = -9
distance = (-3/2)t^2 + 145t/2- 9 , where t is time in hours, and distance is miles
I suspect a typo, and he covered 65 miles the 1st hour.
f(t) = 65t
To write an equation for the relationship between time and distance, we can use the formula:
distance = rate * time
Let's assign variables to the unknowns in the equation:
Let d represent the distance traveled in miles.
Let t represent the time it takes to travel the distance, in hours.
Let r represent the rate or speed at which Lin is driving, in miles per hour.
Now let's write the equations based on the given information:
For the first scenario, when Lin drives 62 miles in 1 hour:
62 = r * 1
For the second scenario, when Lin drives 130 miles in 2 hours:
130 = r * 2
For the third scenario, when Lin drives 195 miles in 3 hours:
195 = r * 3
These three equations represent the relationship between time, distance, and rate of Lin's driving.