Exploring Direct Variation in Algebra

The video tutorial explains how to solve a problem involving direct variation using two methods. The first method involves deriving the direct variation formula and calculating the constant of variation (K) to find the value of Y when X is 45. The second method uses proportions to solve the same problem, demonstrating that both approaches yield the same result. The tutorial emphasizes understanding both methods and choosing the one that suits the learner's preference.

What does it mean when we say that y varies directly with x?

• y increases as x decreases

• y is always equal to x

• y is proportional to x

• y is inversely proportional to x

If y = 6 when x = 30, what is the formula for the direct variation?

• y = kx

• y = 30x

• y = 6x

• y = 1/5x

How do you find the constant k in the direct variation formula y = kx?

• Multiply y by x

• Divide y by x

• Add x to y

• Subtract x from y

What is the value of k if y = 6 when x = 30?

• 1/5

• 5

• 6

• 30

Using the formula y = kx, what is y when x = 45 and k = 1/5?

• 45

• 9

• 30

• 6

What is another method to solve direct variation problems besides finding the formula?

• Using proportions

• Using integrals

• Using logarithms

• Using derivatives

In the proportion method, what is the proportion set up to find y when x = 45?

• y/6 = 45/30

• y/45 = 6/30

• y/30 = 6/45

• y/45 = 30/6

What is the value of y when x = 45 using the proportion method?

• 45

• 9

• 6

• 30

What is the cross product used for in the proportion method?

• To find the value of x

• To find the value of y

• To find the value of k

• To find the value of the ratio

Which method do you prefer for solving direct variation problems?

• Finding the formula

• Using proportions

• Both methods

• Neither method