Direct Variation Worksheet
Is each equation a direct variation? If it is, find the constant of direct variation. If not explain why.
Remember that direct variations have no constants and are of the form y = kx, where k is the
constant of variation (slope). Solve for y and see what you get!
1.
2y = 5x + -1
2.
-x = 10y
3.
-12x = 6y
4.
y + 8 = -x
5.
5x – 6y = 0
6.
- 4 + 7x + 4 = 3y
7. Point A is an element of a direct variation. Identify four points,
other than A, that are also element of the direct variation
(
,
)
(
,
) (
,
)
(
,
)
Are the following tables examples of direct variation? If so state the constant of variation. Hint:
Makes sure that y/x is the same for all points.
8.
9
10.
11.
Are the following graphs examples of direct variation? If yes find the equation, explain if not.
12.
13.
14.
YES
No
Equation
Why?
YES
No
Equation
Why?
YES
No
Equation
Why?
Write an equation of the direct variation that includes the given point.
Find k (k = y/x)
Put k back into y = kx
15.
(-8, 10)
16. (-5, -9)
17. (-5, -10)
18. Given this set of points (1, 10), (3.5, 7), (4, 8), (8, 4), (8, 16), (10, 6). Which points create a relation that is a
direct variation? Find k by dividing y by x. Get all points that have the sake k
19. The weight an object exerts on a scale varies directly with the mass of an object. If a bowling ball has
a mass of 6 kg, the scale reads 54.
a. Write an equation for the relationship between weight and mass.
b. If another object has a mass of 8 kg, what would the scale read?
20. The force you must apply to lift an object varies directly with the objects weight. You would need to
apply 0.5 lbs of force to lift an object that weighs 32 lb.
a. Write an equation for the relationship between force and weight.
b. How much force would you need to lift 160 lbs?