Question

example problem 1: finding the constant of variation. the variable y varies directly with x. if y = 24 when x = 6, write the equation that represents the relationship and find y when x = 10.

Explanation:

Step1: Find the constant of variation

Since $y$ varies directly with $x$, the equation is $y = kx$. When $y = 24$ and $x = 6$, we can find $k$ by substituting these values into the equation: $k=\frac{y}{x}=\frac{24}{6}=4$.

Step2: Write the variation equation

The equation representing the relationship is $y = 4x$.

Step3: Find $y$ when $x = 10$

Substitute $x = 10$ into $y = 4x$, so $y=4\times10 = 40$.

Answer:

The equation is $y = 4x$ and $y = 40$ when $x = 10$.