Direct and Inverse Variation Guided Notes
Name ____________________________________ Date ______________
Objective: Recognize and solve direct and inverse variation problems
Direct Variation
Inverse Variation
1. An equation of the form ______________________, where ________________________.
1. An equation of the form ___________________, where _______________________.
2. As x ______________, y _________________.
2. As x __________________, y ______________.
3. The graph of a direct variation equation is _____________________________ for
all values of x, and passes through the ____________________.
3. The graph of an inverse variation equation is NOT _______________________
for all x-values, and does not have a _________________________.
4. Examples:
4. Examples:
Sketch the graph of …..
Direct Variation
Inverse Variation
Direct and Inverse Variation KEY
Direct Variation
1. An equation of the form 𝑦 = 𝑘 ∙ 𝑥, where 𝑘 ≠ 0
Inverse Variation
𝑘
1. An equation of the form 𝑦 = 𝑥, where 𝑘 ≠ 0
2. As x increases, y increases.
2. As x increases, y decreases.
3. The graph of a direct variation equation is continuous for all values of x
and passes through the origin.
3. The graph of an inverse variation equation is NOT continuous for all xvalues and does not have a y-intercept.
4. Examples:
a) hours worked and pay
b) distance and time
c) iTunes (amount of songs purchased and total amount spent)
d) length of sides of a figure and perimeter of the figure
4. Examples:
a) time it takes for ice to melt varies inversely with the temperature
b) Number of people eating pizza and number of pieces of pizza available
per person
c) length and width of a rectangle if the area remains constant
𝑦 = 3𝑥
5
𝑦=𝑥