Understanding Direct Variation and Proportions

Which of the following best describes the relationship between speed and time in a graph of direct variation? a) The graph is a curve b) The graph is a straight line passing through the origin c) The graph is a straight line not passing through the origin d) The graph is a horizontal line

• The graph is a straight line passing through the origin

• The graph is a vertical line

• The graph is a zigzag line

• The graph is a dotted line

In a direct variation, if y=15 when x=3, what is the constant of proportionality k? a) 5 b) 3 c) 45 d) 9

• 10

• 5

• 12

• 20

If the current I passing through a resistor is inversely proportional to its resistance R, what happens to I if R is doubled? a) I is doubled b) I is halved c) I remains constant d) I is squared

• I is reduced by a quarter

• b) I is halved

• I is tripled

• I becomes zero

According to Hooke's Law, what is the relationship between stress S and strain δ within the elastic limit? a) Stress is inversely proportional to strain b) Stress is directly proportional to strain c) Stress is equal to strain d) Stress is proportional to the square of strain

• Stress is proportional to the cube of strain

• Stress is independent of strain

• Stress is inversely proportional to the square of strain

• b) Stress is directly proportional to strain

Which of the following formulas correctly expresses the Pythagorean theorem?

• a) a² + b² = c²

• a² + b = c²

• a + b² = c²

• a² + b² = c

If y varies directly with x and y = 20 when x = 4, what is the value of y when x = 10?

• 100

• 30

• 80

• 50

In a direct variation, if k = 8 and x = 5, what is the value of y?

• 10

• 40

• 25

• 35

If the temperature T is directly proportional to the amount of heat Q, what happens to T if Q is tripled?

• T is unchanged

• T is doubled

• T is decreased

• T is tripled

Which of the following statements is true about direct variation? a) It can be represented by a quadratic equation b) It always passes through the origin c) It can have negative values only d) It is not a linear relationship

• a) It can be represented by a cubic equation

• b) It always passes through the origin

• c) It can only have positive values

• d) It is a non-linear relationship

If the distance d varies directly with time t and d = 100 when t = 2, what is the distance when t = 5?

• 250

• 400

• 100

• 150