Math Problem Statement
Determine the constant of proportionality and write the direct variation equation for the ordered pairs (10, -2) and (90, -18).
Solution
To solve the problem, we need to determine the constant of proportionality () for the given ordered pairs and and then express the direct variation equation.
Step 1: Formula for direct variation
The relationship for direct variation is given by: where is the constant of proportionality.
To find , we can use the formula:
Step 2: Compute for each ordered pair
-
For :
-
For :
Since is consistent for both points, the constant of proportionality is:
Step 3: Write the direct variation equation
Using the formula and substituting :
Final Answer:
- The constant of proportionality () is .
- The direct variation equation is:
Would you like further details or examples?
Here are 5 related questions to deepen your understanding:
- How can we verify that the equation holds for other values of ?
- What are some real-life examples of direct variation?
- Can you identify the graph shape of a direct variation equation like ?
- What happens if in a direct variation?
- How do you solve for given in ?
Tip: Always double-check by substituting back into the equation with both ordered pairs!
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Math Problem Analysis
Mathematical Concepts
Direct Variation
Proportionality
Algebra
Formulas
y = kx
k = y/x
Theorems
Direct Variation Theorem
Suitable Grade Level
Grades 7-9