1. Write and graph a direct variation equation
EXAMPLE 1
Write and graph a direct variation equation
Write and graph a direct variation equation that has
(– 4, 8) as a solution.
SOLUTION
Use the given values of x and y to find the constant of
variation.
y = ax
Write direct variation equation.
8 = a(– 4)
Substitute 8 for y and – 4 for x.
–2= a
Solve for a.

2. EXAMPLE 1
Write and graph a direct variation equation
ANSWER
Substituting – 2 for a in y = ax gives the direct variation equation y = – 2x. Its graph is shown.

3. Use the given values of x and y to find the constant of variation.
GUIDED PRACTICE
for Example 1
Write and graph a direct variation equation that has the given ordered pair as a solution.
(3, – 9)
SOLUTION
Use the given values of x and y to find the constant of
variation.
y = ax
Write direct variation equation.
–9 = a(3)
Substitute – 9 for y and 3 for x.
–3= a
Solve for a.

4. GUIDED PRACTICE
for Example 1
ANSWER
Substituting – 3 for a in y = ax gives the direct variation equation y = – 3x. Its graph is shown.

5. Use the given values of x and y to find the constant of variation.
GUIDED PRACTICE
for Example 1
Write and graph a direct variation equation that has the given ordered pair as a solution.
(– 7, 4)
SOLUTION
Use the given values of x and y to find the constant of
variation.
y = ax
Write direct variation equation.
4 = a(– 7)
Substitute 4 for y and – 7 for x.
– 4 7
= a
Solve for a.

6. GUIDED PRACTICE
for Example 1
ANSWER
Substituting for a in y = ax gives the direct variation
equation y = x. Its graph is shown. 7
– 4

7. Use the given values of x and y to find the constant of variation.
GUIDED PRACTICE
for Example 1
Write and graph a direct variation equation that has the given ordered pair as a solution.
(5, 3)
SOLUTION
Use the given values of x and y to find the constant of
variation.
y = ax
Write direct variation equation.
3 = a(5)
Substitute 3 for y and 5 for x.
= a 5 3
Solve for a.

8. GUIDED PRACTICE
for Example 1
ANSWER
Substituting for a in y = ax gives the direct variation
equation y = x. Its graph is shown. 5 3

9. Use the given values of x and y to find the constant of variation.
GUIDED PRACTICE
for Example 1
Write and graph a direct variation equation that has the given ordered pair as a solution.
(6, – 2)
SOLUTION
Use the given values of x and y to find the constant of
variation.
y = ax
Write direct variation equation.
– 2 = a(6)
Substitute – 2 for y and 6 for x.
= a 3
– 1
Solve for a.

10. GUIDED PRACTICE
for Example 1
ANSWER
Substituting for a in y = ax gives the direct variation
equation y = x. Its graph is shown. 3
– 1