Application problem with a linear function: Finding a coordinate given two points

Question

Henry is driving to Memphis. Suppose that the distance to his destination (in miles) is a linear function of his total driving time (in minutes). Henry has
56
miles to his destination after
45
minutes of driving, and he has
32.2
miles to his destination after
73
minutes of driving. How many miles will he have to his destination after
77
minutes of driving?

 

find how many miles?

 

Answer 1

your function will be in the form:

f(x) = mx + b

 

where f(x) is the distance to destination and x is minutes of driving

 

(45,56)

(73, 32.2)

(77,?)

 

find slope using first two coordinates

(32.2-56)/(73-45) = -0.85

 

y=mx+b

y=b-0.85x 

find b with either coordinate

y+0.85x = b

56+0.85(45) = b

94.25 = b

 

the function is 

f(x) = 94.25-0.85x

 

so f(77) = 94.25-0.85(77) = 28.8 miles to destination