Math Problem Statement
If y varies directly as x, and y = 7 when x = 6, find y when x = 18.
Solution
The problem states that "y varies directly as x," meaning that there is a direct proportional relationship between and , which can be expressed as:
where is the constant of proportionality.
We are given that when . Let's use this to find :
Now that we have , we can find when :
So, when , .
Do you need more details on any part of the explanation? Here are five related questions to expand your understanding:
- What is the difference between direct and inverse variation?
- Can you express direct variation as a ratio between two variables?
- How would you find if you were given and the constant ?
- What happens to if is doubled in a direct variation?
- How can you graph a direct variation equation like this one?
Tip: In a direct variation, as one variable increases, the other increases proportionally, and the ratio between them remains constant.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Direct Proportionality
Algebra
Formulas
y = kx
Theorems
Direct Variation Theorem
Suitable Grade Level
Grades 7-9