Answer: d = 111t
Step-by-step explanation:Given that the car is moving at a constant speed, we can use the formula for linear functions to model the distance in feet d the car has traveled any number of seconds t after passing the timing device. A linear function is a function in which the highest power of the unknown variable is one. The linear function with dependent variable d and independent variable t can be written as:
d = mt + b
where m is the slope of the function and b is the y-intercept. To find the slope of the function, we can use the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line. In this case, we have two points: (0, 0) and (7, 777). Therefore, the slope of the function is:
m = (777 - 0) / (7 - 0) = 111
To find the y-intercept, we can use the fact that the car passed the timing device at t = 0, which means that d = 0 when t = 0. Therefore, the y-intercept is:
b = 0
Substituting the values of m and b into the equation for the linear function, we get:
d = 111t
Therefore, the linear function rule to model the distance in feet d the car has traveled any number of seconds t after passing the timing device is:
d = 111t