Slope and Direct Variation Lesson 5-2. ____________ ______________ is an equation in the form of...
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Transcript of Slope and Direct Variation Lesson 5-2. ____________ ______________ is an equation in the form of...
![Page 1: Slope and Direct Variation Lesson 5-2. ____________ ______________ is an equation in the form of ________, where k≠0. In the equation y = kx, ____ is.](https://reader035.fdocuments.net/reader035/viewer/2022081603/5697bffa1a28abf838cc01e0/html5/thumbnails/1.jpg)
Slope and Direct Variation
Lesson 5-2
![Page 2: Slope and Direct Variation Lesson 5-2. ____________ ______________ is an equation in the form of ________, where k≠0. In the equation y = kx, ____ is.](https://reader035.fdocuments.net/reader035/viewer/2022081603/5697bffa1a28abf838cc01e0/html5/thumbnails/2.jpg)
____________ ______________ is an equation in the form of ________,
where k≠0. In the equation y = kx, ____ is the ______________________.
(k is always equal to the __________________ .) Direct variation is also
known as a direct __________________________.
Direct variation y = kx
k constant of variation
slope
proportion
![Page 3: Slope and Direct Variation Lesson 5-2. ____________ ______________ is an equation in the form of ________, where k≠0. In the equation y = kx, ____ is.](https://reader035.fdocuments.net/reader035/viewer/2022081603/5697bffa1a28abf838cc01e0/html5/thumbnails/3.jpg)
1
up 1 right 1
A direct variation will ALWAYS pass through the origin.
![Page 4: Slope and Direct Variation Lesson 5-2. ____________ ______________ is an equation in the form of ________, where k≠0. In the equation y = kx, ____ is.](https://reader035.fdocuments.net/reader035/viewer/2022081603/5697bffa1a28abf838cc01e0/html5/thumbnails/4.jpg)
Graph y = 2x
m = _______
•Remember, the first point will always be (0,0) in a direct variation.•Find additional points using the slope.
![Page 5: Slope and Direct Variation Lesson 5-2. ____________ ______________ is an equation in the form of ________, where k≠0. In the equation y = kx, ____ is.](https://reader035.fdocuments.net/reader035/viewer/2022081603/5697bffa1a28abf838cc01e0/html5/thumbnails/5.jpg)
up 3
left 2
![Page 6: Slope and Direct Variation Lesson 5-2. ____________ ______________ is an equation in the form of ________, where k≠0. In the equation y = kx, ____ is.](https://reader035.fdocuments.net/reader035/viewer/2022081603/5697bffa1a28abf838cc01e0/html5/thumbnails/6.jpg)
Moving up 2 and left 3 will fall on the same line as moving down 2 and right 3.
![Page 7: Slope and Direct Variation Lesson 5-2. ____________ ______________ is an equation in the form of ________, where k≠0. In the equation y = kx, ____ is.](https://reader035.fdocuments.net/reader035/viewer/2022081603/5697bffa1a28abf838cc01e0/html5/thumbnails/7.jpg)
![Page 8: Slope and Direct Variation Lesson 5-2. ____________ ______________ is an equation in the form of ________, where k≠0. In the equation y = kx, ____ is.](https://reader035.fdocuments.net/reader035/viewer/2022081603/5697bffa1a28abf838cc01e0/html5/thumbnails/8.jpg)
![Page 9: Slope and Direct Variation Lesson 5-2. ____________ ______________ is an equation in the form of ________, where k≠0. In the equation y = kx, ____ is.](https://reader035.fdocuments.net/reader035/viewer/2022081603/5697bffa1a28abf838cc01e0/html5/thumbnails/9.jpg)
y = kx
9 -3 9 = k (-3)
-3 = k
y = -3x
y = -3x
15 = -3x
-5 = x
![Page 10: Slope and Direct Variation Lesson 5-2. ____________ ______________ is an equation in the form of ________, where k≠0. In the equation y = kx, ____ is.](https://reader035.fdocuments.net/reader035/viewer/2022081603/5697bffa1a28abf838cc01e0/html5/thumbnails/10.jpg)
y = kx
15 = k(5)
15/5 = 5k/5
3 = k
y = 3x
y = 3x
-45 = 3x
-45/3 = (3x)/3
-15= x
![Page 11: Slope and Direct Variation Lesson 5-2. ____________ ______________ is an equation in the form of ________, where k≠0. In the equation y = kx, ____ is.](https://reader035.fdocuments.net/reader035/viewer/2022081603/5697bffa1a28abf838cc01e0/html5/thumbnails/11.jpg)
Practice: Write a direct variation equation that relates x and y. Assume that y varies directly as x. Then solve.
7. If y = 27 when x = 6, 8. If y = 10 when x = 9, find x when y = 45. find x when y = 9. ________________________ ____________________
________________________ ___________________
________________________ ______________________
________________________ ______________________
________________________ ______________________
________________________ ______________________
________________________ ______________________
![Page 12: Slope and Direct Variation Lesson 5-2. ____________ ______________ is an equation in the form of ________, where k≠0. In the equation y = kx, ____ is.](https://reader035.fdocuments.net/reader035/viewer/2022081603/5697bffa1a28abf838cc01e0/html5/thumbnails/12.jpg)
Practice: Write a direct variation equation that relates x and y. Assume that y varies directly as x. Then solve.
9. If y = -7 when x = 14, 10. find y when x = 20. ________________________ ______________________
________________________ ______________________
________________________ ______________________
________________________ ______________________
________________________ ______________________
________________________ ______________________
________________________ ______________________
![Page 13: Slope and Direct Variation Lesson 5-2. ____________ ______________ is an equation in the form of ________, where k≠0. In the equation y = kx, ____ is.](https://reader035.fdocuments.net/reader035/viewer/2022081603/5697bffa1a28abf838cc01e0/html5/thumbnails/13.jpg)
Using Direct Variations to Solve ProblemsThe Ramirez family is driving cross-country on vacation. They drive 330 miles in 5.5 hours.
A. Write a direct variation equation to find the distance driven for any number of hours.
y = 60 x
10 hours
![Page 14: Slope and Direct Variation Lesson 5-2. ____________ ______________ is an equation in the form of ________, where k≠0. In the equation y = kx, ____ is.](https://reader035.fdocuments.net/reader035/viewer/2022081603/5697bffa1a28abf838cc01e0/html5/thumbnails/14.jpg)
A flock of geese migrated 375 miles in 7.5 hours. A. Write a direct variation equation to find the distance flown in any time.
y = 50 x
B. Estimate how many hours of flying time it would take the geese to migrate 3000 miles.
y = distance, x = time in hours
y = 50 x
3000 = 50 x
60 hours = x