Understanding Direct and Inverse Variation

The video tutorial explains the concepts of direct and inverse variation. It begins with a problem where y varies directly with x, solving for the constant k and then finding y when x is 15. The tutorial then shifts to inverse variation, specifically with the square of x, solving for k and finding y when x is 4. The instructor also encourages viewers to subscribe and provides additional resources for further learning.

What does it mean when y varies directly with x?

• y is equal to k times x

• y is equal to k divided by x

• y is equal to k minus x

• y is equal to x divided by k

If y is 21 when x is 9, what is the value of k in the equation y = kx?

• 3

• 7/3

• 21/9

• 9/21

What is the value of y when x is 15, given y = 7/3 * x?

• 15

• 45

• 21

• 35

What mistake was corrected in the calculation of y when x is 15?

• Using the wrong value of k

• Dividing by 3 instead of multiplying

• Multiplying 7 by 3 instead of 5

• Multiplying 7 by 5 incorrectly

How does y vary with x in inverse variation with the square of x?

• y is equal to k times x squared

• y is equal to k divided by x squared

• y is equal to k times x

• y is equal to k divided by x

What is the formula for y when it varies inversely with x?

• y = x/k

• y = kx^2

• y = kx

• y = k/x

If y equals 2 when x is 2, what is the value of k in the equation y = k/x^2?

• 4

• 8

• 16

• 2

What is the value of y when x is 4, given y = 8/x^2?

• 1/2

• 2

• 1

• 4

What is the relationship between y and x when y varies inversely with x squared?

• y increases as x increases

• y decreases as x increases

• y remains constant as x changes

• y is directly proportional to x

What is the first step in solving for y when given a direct or inverse variation problem?

• Multiply y by x

• Calculate the value of y

• Solve for x

• Determine the constant k