Respuesta :
Part A:
The y-intercept of the function is given when x = 0. We already have a y-value for x = 0, and that y-value is 330.
Assuming miles is the unit used here for distance, this means that the truck was started 330 miles away from its destination.
Part B:
The average rate of change is represented by the slope of this function. We can find the slope of this function with the rise over run formula:
[tex] \frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]
We are asked to use the points at x = 1 and x = 4. Plug the x and y values into the formula:
(1,275) and (4,110)
[tex] \frac{110-275}{4-1} = \frac{-165}{3} = -55[/tex]
The average rate of change of the function is -55. This represents the average miles per hour the truck travels towards its destination.
Part C:
This part asks for the x-intercept of the equation. The x-intercept is defined where y = 0, which represents the destination the truck is traveling to. The domain would be restricted by the y-intercept and x-intercept, as the truck stops once it reaches its destination. We are missing the x-intercept, so we'll use the slope and the y-intercept to find it.
To find the x-intercept, we must divide the y-intercept by the slope, and subtract the result from the y-intercept's x-value:
[tex]330 \div -55 = -6[/tex]
[tex]0 - (-6) = 6[/tex]
The x-intercept is located at (6,0). The domain can be stated as follows:
[tex]\{x| 0 \leq x \leq 6\}[/tex]
The y-intercept of the function is given when x = 0. We already have a y-value for x = 0, and that y-value is 330.
Assuming miles is the unit used here for distance, this means that the truck was started 330 miles away from its destination.
Part B:
The average rate of change is represented by the slope of this function. We can find the slope of this function with the rise over run formula:
[tex] \frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]
We are asked to use the points at x = 1 and x = 4. Plug the x and y values into the formula:
(1,275) and (4,110)
[tex] \frac{110-275}{4-1} = \frac{-165}{3} = -55[/tex]
The average rate of change of the function is -55. This represents the average miles per hour the truck travels towards its destination.
Part C:
This part asks for the x-intercept of the equation. The x-intercept is defined where y = 0, which represents the destination the truck is traveling to. The domain would be restricted by the y-intercept and x-intercept, as the truck stops once it reaches its destination. We are missing the x-intercept, so we'll use the slope and the y-intercept to find it.
To find the x-intercept, we must divide the y-intercept by the slope, and subtract the result from the y-intercept's x-value:
[tex]330 \div -55 = -6[/tex]
[tex]0 - (-6) = 6[/tex]
The x-intercept is located at (6,0). The domain can be stated as follows:
[tex]\{x| 0 \leq x \leq 6\}[/tex]
Part A: The y-intercept of the linear graph is when x=0. So, from our date, the y-intercept is at y=330
Part B: The rate of change is 55 and it represents the decrease of 55 miles for every hour travelled
Part C: The domain of the function will be meaning the traveller will reach its destination after travelling hours (assuming the traveller doesn't stop for break)
