Question

A car moving at a constant speed passes a timing device at t=0. After 8 seconds the car has traveled 840 feet. what linear function in the form y=mx+b represents the distance in the feet, d, the car has traveled any number of seconds, t, after passing the timing device?

Answer 1

at t=0 the car has moved 0 feet, also you know it has a constant speed so you get the points:

P1:(0,0) therefore you know b, the y-intercept=0
P2:(8,840)

insert P2 into y=mx+b
840=8m+0
840/8=m
105=m

so the result is:
y=105x=105t=f(t)=d

Answer 2

Linear function for the car which moves with the constant speed and passes through a timing device is,

$d=105t$

What is linear function?

Linear function is the function in which the highest power of the unknown variable is one. Linear functions are used to model the real life problem in the mathematical expressions.

The linear function with dependent variable y and independent variable x can be written as,

$y=mx+b$

Here, (m) is the slope of the function and (b) is the y intercept.

As the car is moving at a constant speed passes a timing device at t=0.

After 8 seconds the car has traveled 840 feet.

To construct the equation of linear function, we have to find the point of it.

One point of the line is (0, 0) as the car move 0 distance at 0 time.

Another point of the line is (8, 840) as after 8 seconds the car has traveled 840 feet.

From the equation of linear line,

$(y-0)=\dfrac{840-0}{8-0}(x-0)\\y=105x$

Here, the s the distance in the feet, d, the car has traveled any number of seconds, t, after passing the timing device. Thus the function can be written as,

$d=105t$

Thus the linear function in the form y=mx+b represents the distance in the feet, d, the car has traveled any number of seconds, t is,

$d=105t$

Learn more about the linear function here;

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