a Using the given information, find two points that solve the equation. Use them to write the equation in point-slope form.
B
b Use the Distance Formula to calculate Alberto's speed. Remember to express the speed in miles per hour.
A
a 350 feet
B
b No, see solution.
Practice makes perfect
a We are going to write the equation for this situation in point-slope form and then use it to calculate the height above the bottom of the slope at 10 seconds. To do this, we will let x be the number of seconds that have passed and y will be the corresponding heights.
Write The Equation
To find the slope of the equation, we need two points that lie on the line. We know that Alberto began at a height of 4600 feet. Since 0 seconds had passed at that time, we can create the point (0,4600). For a second point, we can use that, after 24 seconds, he reaches the bottom of the hill. We are told that the bottom of the hill is 600 feet lower than the top.
4600-600=4000feetThis gives a second point, (24,4000). Now we can use the Slope Formula.
Now, we can substitute the value of the slope and one of the points, let's use (0,4600), into the point-slope form of the equation.
y-4600=- 25(x-0) ⇔ y-4600=- 25x
Calculate The Height
In our equation, x represents the number of seconds Alberto is snowboarding. Therefore, to calculate his height above the bottom of the hill at 10 seconds into the run, we substitute x with 10 and solve for y.
Alberto is going to be at a height of 4350 feet. Since the bottom of the hill is at 4000 feet, we can subtract this number from 4350 to calculate his height above the bottom of the hill.
4350-4000=350feet
After 10 seconds of snowboarding, Alberto will be 350 feet above the bottom of the hill.
b Let's calculate Alberto's speed and see if he's correct. To calculate the speed, we can use the Distance Formula.
distance=rate*time ⇒ d=rt
The length of the hill that Alberto is snowboarding down is 1560 feet and it takes him 24 seconds to travel this distance. Let's substitute 1560 for d and 24 for t into the formula and calculate the rate (speed).
Alberto's speed is 65 fts. Alberto thinks that his speed is equal to 50 miles per hour. To compare and verify, we should express his speed in miles per hour. Remember that 1 mile equals 5280 feet and 1 hour is equal to 3600 seconds. This gives us the following conversion factors.
1mile/5280ft and 3600sec/1hr
If we multiply these conversion factors by his speed, we will have it in miles per hour.
