Respuesta :
Part A
x = number of hours the scooter is rented
y = total rent (in dollars)
"Amir rented a scooter at $43 for 3 hours" means x = 3 and y = 43 giving the point (3,43)
"he rents the same scooter for 8 hours, he has to pay a total rent of $113" means x = 8 pairs up with y = 113. The second point is (8,113)
The two points (3,43) and (8,113) can be used to find the slope
m = (y2 - y1)/(x2 - x1)
m = (113 - 43)/(8 - 3)
m = (70)/(5)
m = 14
The slope of 14 tells us that it costs $14 per hour to rent the scooter
If we simply consider the hourly cost of $14 per hour (and no additional fees), then the cost break down would look like this:
1 hour costs Amir $14
2 hours costs Amir $28 (2*14 = 28)
3 hours costs Amir $42 (3*14 = 42)
If we don't have any fixed costs, then it would cost Amir $42 total to rent the scooter for 3 hours. But it says the cost is actually 43 dollars. So the fixed cost, the y intercept, must be 1 dollar. Think of the $1 as the fee that Amir pays to get into the park or maybe as some kind of insurance. This fixed fee is not dependent on the number of hours Amir rents the scooter.
In other words, if m = 14, x = 3 and y = 43, then
y = mx+b
43 = 14*3+b
43 = 42+b
b = 1
Making the equation to be y = 14x+1
Answer: y = 14x+1
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Part B
All we do here is go from y = 14x+1 to f(x) = 14x+1. We simply replace y with f(x) to get it into function notation.
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Part C
The y intercept is 1 as this is the value of b in y = mx+b. Compare this to y = 14x+1.
Another way to look at this is that if we plug in x = 0 into y = 14x+1, we get y = 1. So the point (0,1) is on the function. This is where the graph crosses the y axis.
Starting at (0,1) go up 14 units and then to the right 1 unit. You'll arrive at (1,15) as the next point on this graph. Draw a straight line through (0,1) and (1,15) to complete the graph of y = 14x+1
You should have "number of hours" along the x axis and "cost (in dollars)" along the y axis for your proper labels. As for intervals, I would increment x by 1 each time (0, 1, 2, 3, ...) and increment y by 2 at the smallest or 5 at the largest. It will depend on your preference really.
x = number of hours the scooter is rented
y = total rent (in dollars)
"Amir rented a scooter at $43 for 3 hours" means x = 3 and y = 43 giving the point (3,43)
"he rents the same scooter for 8 hours, he has to pay a total rent of $113" means x = 8 pairs up with y = 113. The second point is (8,113)
The two points (3,43) and (8,113) can be used to find the slope
m = (y2 - y1)/(x2 - x1)
m = (113 - 43)/(8 - 3)
m = (70)/(5)
m = 14
The slope of 14 tells us that it costs $14 per hour to rent the scooter
If we simply consider the hourly cost of $14 per hour (and no additional fees), then the cost break down would look like this:
1 hour costs Amir $14
2 hours costs Amir $28 (2*14 = 28)
3 hours costs Amir $42 (3*14 = 42)
If we don't have any fixed costs, then it would cost Amir $42 total to rent the scooter for 3 hours. But it says the cost is actually 43 dollars. So the fixed cost, the y intercept, must be 1 dollar. Think of the $1 as the fee that Amir pays to get into the park or maybe as some kind of insurance. This fixed fee is not dependent on the number of hours Amir rents the scooter.
In other words, if m = 14, x = 3 and y = 43, then
y = mx+b
43 = 14*3+b
43 = 42+b
b = 1
Making the equation to be y = 14x+1
Answer: y = 14x+1
---------------------------------------------------------------
Part B
All we do here is go from y = 14x+1 to f(x) = 14x+1. We simply replace y with f(x) to get it into function notation.
---------------------------------------------------------------
Part C
The y intercept is 1 as this is the value of b in y = mx+b. Compare this to y = 14x+1.
Another way to look at this is that if we plug in x = 0 into y = 14x+1, we get y = 1. So the point (0,1) is on the function. This is where the graph crosses the y axis.
Starting at (0,1) go up 14 units and then to the right 1 unit. You'll arrive at (1,15) as the next point on this graph. Draw a straight line through (0,1) and (1,15) to complete the graph of y = 14x+1
You should have "number of hours" along the x axis and "cost (in dollars)" along the y axis for your proper labels. As for intervals, I would increment x by 1 each time (0, 1, 2, 3, ...) and increment y by 2 at the smallest or 5 at the largest. It will depend on your preference really.
