Name _________________________________________________________ Date _________
Enrichment- Direct Variation, Inverse Variation, or Neither?
3.8
Without graphing, you can tell whether a table of data shows direct variation, inverse variation,
or neither.
y  kx Direct variation equation
y
Solve for k.
k 
x
k
Inverse variation equation
x
k  xy Solve for k.
y 
With direct variation, the ratio of y to x is constant for all ordered pairs except 0, 0. With inverse
variation, the product xy is constant for all ordered pairs.
Example: Without graphing, tell whether x and y
show direct variation, inverse variation, or neither.
x
–10
–5
–1
1
5
10
y
–0.5
–1
–5
5
1
0.5
Find the products xy for each ordered pair.
10 0.5  5
51  5
15  5
51  5
100.5  5
Because the products xy are constant, the data shows inverse variation.
Check:
1
1

5
5
0.5
1

10
20
The ratios are different. So, the data does not show direct variation.
Without graphing, tell whether x and y show direct variation, inverse variation, or neither.
Explain your reasoning.
1.
3.
5.
144
2.
x
–5
–3
–1
1
y
–9
–5
–1
3
x
–12
–9
–6
–3
y
4
3
2
1
x
1
2
3
6
y
6
3
2
1
4.
6.
x
–8
–4
0
4
y
–2
–1
0
1
x
–15
–12
–6
–3
y
0.2
0.25
0.5
1
x
0
1
2
3
4
5
y
0
1
4
9
15
25
Big Ideas Math Red