Question

henry is driving to Boston. Suppose that the remaining distance to drive in miles is a linear function of his driving time in minutes). When graphed, the function gives a line with a slope of -0.95. Henry has 55 miles remaining after 44 minutes of driving. How many miles will be remaining after 64 minutes of driving.

Answer 1

when it says that remaining distance is a linear function of time, this means that the remaining distance depends on time. since we know y depends on x we will say remaining distance is y and time is x. so we have a basic equation of
y = mx + b

where slope is m, y is remaining distance, x is time, and b is a constant

it says the slope of lineis -0.95. sub that in for m and get
y = -0.95x + b

it says 55 remaining distance after 44 time. so we have a x and y
55 = -0.95 (44) + b
55 = -41.8 + b
96.8 = b

we now have b
y = -0.95x + 96.8

it asks for remaining distance after 64 time. we have an x and must solve for y
y = -0.95 (64) + 96.8
y = 36 miles