Question

I'm studying for my algebra test and I'm stuck on a problem about direct variation. I have a table of values for x and y, but I'm not sure if y varies directly with x or how to write the equation if it does. Can you find an example of a similar problem and its solution on the Questions.llc website? The table I have is x = 4, 6, 8 and y = 28, 48, 72.

Answer 1

Sure! To determine if \( y \) varies directly with \( x \), you need to see if you can express \( y \) as a constant multiple of \( x \). A direct variation means that \( y = kx \), where \( k \) is a constant.

Using the data you provided:

- When \( x = 4 \), \( y = 28 \):
\[
k = \frac{y}{x} = \frac{28}{4} = 7
\]

- When \( x = 6 \), \( y = 48 \):
\[
k = \frac{y}{x} = \frac{48}{6} = 8
\]

- When \( x = 8 \), \( y = 72 \):
\[
k = \frac{y}{x} = \frac{72}{8} = 9
\]

Since the value of \( k \) is not constant across the different pairs of \( x \) and \( y \), we can conclude that \( y \) does not vary directly with \( x \).

In summary, the relationship does not appear to be a direct variation. If you have a specific example on Questions.llc you want to explore further, you would need to look it up directly on their website since I can’t access external sites. However, I can help you solve more similar problems or clarify concepts if needed!