Exploring Direct, Inverse, and Joint Variation

What happens to the area of a rectangle if the width is fixed at 2 and the length increases?

• Area increases

• Area decreases

• Area remains constant

• Area becomes zero

What shape does the graph form when plotting length against area in a direct variation scenario?

• Straight line

• Hyperbola

• Circle

• Parabola

In an inverse variation, if the length of a rectangle is increased, what happens to the width if the area is constant?

• Width increases

• Width remains constant

• Width decreases

• Width becomes zero

What is the equation form for direct variation?

• y = k + x

• y = x/k

• y = kx

• y = k/x

How do you find the constant of variation when given specific values for y and x in a direct variation?

• Add y to x

• Divide y by x

• Multiply y by x

• Subtract y from x

In a word problem, if the weight of a load of bricks varies directly with the number of bricks, what happens to the weight if the number of bricks doubles?

• Weight halves

• Weight remains the same

• Weight doubles

• Weight increases by a factor of four

What is the relationship between volume of a gas, its temperature, and pressure?

• Directly proportional to temperature and pressure

• Inversely proportional to temperature and directly to pressure

• Inversely proportional to both temperature and pressure

• Directly proportional to temperature and inversely to pressure

What does joint variation involve?

• No variables varying

• Multiple variables varying directly together

• One variable varying inversely as another

• One variable varying directly as another

In joint variation, if one variable is squared in the equation, what does this imply about its relationship to the output?

• It has an exponential effect

• It has a diminishing effect

• It has a neutral effect

• It has a direct effect

How do you solve for an unknown in a variation equation when given specific values for other variables?

• Substitute and solve using multiplication

• Substitute and solve using addition

• Substitute and solve using subtraction

• Substitute and solve using division