We are asked to find the linear function that represents the distance the car has traveled any number of seconds after passing the timing device. The desired linear function has to follow a specific format.
y= m x+ b
In this case, y is represented by d and x is represented by t.
d= m t+ b
For an equation in this form, m is the slope and b is the y-intercept. To find the desired linear function we will calculate the slope and the y-intercept. We can do this by using any two points lying on the line that is the graph of the linear function. Let's go through the content of the exercise and get the points we need!
Sentence From the Exercise
Point (t,d)
A car moving at a constant speed passes a timing device at t= 0.
( 0, 0)
After 8 seconds, the car has traveled 840 feet.
( 8, 840)
Now we can use the obtained points to calculate m. We will start by substituting the points into the Slope Formula.
In our function, a slope of 105 means that each second the car travels 105 feet. Now that we know the slope, we can write a partial version of the equation.
d= 105 t+ b
To complete the equation, we also need to determine the y-intercept b. Since we know that the given points will satisfy the equation, we can substitute one of them into the equation to solve for b. Let's use ( 0, 0).
