Guided Notes: Direct Variation
Name_________________________
Direct Variation—a function of the form __________________, where k ≠ 0.


k is the “____________________________________________ ” (It is the coefficient of x)
When graphed, the y-intercept (b) is ________________.
Example 1: Graph the direct variation below:
Example 2: Write the equation of the direct
variation graphed below:
2
𝑦= 𝑥
3
y-intercept = _____
slope = __________
y-intercept = _____
Direct Variation =
slope = __________
________________
__________________________________________________________________________________________
Example 3: y = 3x
Example 4: y = -x
Constant of Variation: ______
Constant of Variation: ________
Tell whether the equation is an example of direct variation. If it is, find the constant of variation.
1. y = 2x
2. 2x + 5y = 1
YES or NO
YES or NO
k = _____
k = _____
3. 5x – 6y = 0
4. -x = 10y
YES or NO
YES or NO
k = _____
k = _____
Write an equation of direct variation that includes the given point:
7. (1, 5)
y = __________
8. (-8, 10)
y = __________
Assume that y varies directly with x:
9. If y = 28 when x = 7, find x when y = 52
10. If
= when
= , find y when
Direct Variation = __________
Direct Variation = __________
x = ______________________
x = ______________________
=
Direct Variation Applications
11. The income at a store varies directly as the advertising budget. When the owners spent $2300 per month
to advertise, their monthly gross income was $120,000. If the owners increase their advertising budget to
$5000 per month, how much gross monthly income can they expect?
12. The length that a spring will stretch S varies directly with the weight w attached to the spring. If a spring
stretches 11 inches when a 20 pound weight is attached, how far will it stretch when a 10 pound weight is
attached?