Direct Variation Concepts and Problems

The video tutorial introduces the concept of direct variation, explaining that when y varies directly with x, it follows the formula y = kx. The tutorial provides an example problem where y is 10 when x is 5, and guides viewers through solving for the constant k. The process involves dividing y by x to find k, and then using this value to write the direct variation equation. The tutorial emphasizes understanding the formula and its application, comparing it to the slope-intercept form of a line equation.

What is the relationship between Y and X in a direct variation?

• Y is directly proportional to X

• Y is inversely proportional to X

• Y is unrelated to X

• Y is equal to X squared

In the formula y = kx, what does 'k' represent?

• The slope

• The constant of variation

• The x-intercept

• The y-intercept

How is the direct variation formula similar to the slope-intercept form?

• Both have a slope, but direct variation has no y-intercept

• Both have a variable term

• Both have a constant term

• Both are quadratic equations

What happens to the y-intercept in a direct variation equation?

• It is equal to K

• It varies with X

• It is always 1

• It is always 0

Which of the following is NOT a characteristic of direct variation?

• The constant K is the slope

• The equation has a y-intercept

• The graph is a straight line through the origin

• Y is directly proportional to X

What is the general form of a direct variation equation?

• y = k/x

• y = mx + b

• y = kx

• y = x^2 + k

What is the first step in solving for K in a direct variation problem?

• Add Y and X

• Multiply Y by X

• Subtract X from Y

• Divide Y by X

If Y is 10 and X is 5, what is the value of K?

• 1

• 10

• 2

• 5

After finding K, what is the next step in forming the direct variation equation?

• Add K to X

• Subtract K from Y

• Plug K back into the formula

• Divide K by X

What is the final equation if K is found to be 2?

• y = 2x

• y = x + 2

• y = 2 + x

• y = x - 2