In the regression equation y = mx + b, y increases with x in all cases:

Question

Options

• AIf b is positive
• BIf b is negative
• CIf m is positive
• DIf m is negative

• A
  2% (1)
• B
  3% (2)
• C
  92% (54)
• D
  3% (2)

Explanation

Option C is correct because m is the slope - it determines the rate and direction of change between x and y. When m is positive, every unit increase in x produces a proportional increase in y, making the relationship strictly increasing regardless of any other values.

Options A and B are wrong because b is the y-intercept, which only shifts the line up or down on the graph - it has no effect on the direction or steepness of the relationship between x and y. Option D is wrong because a negative m means y decreases as x increases (a downward-sloping line).

Memory tip: Think of m as "movement" - it controls how y moves as x changes. Positive m = moving up; negative m = moving down. The letter b is just where the line begins (crosses the y-axis), so it can never change the slope's direction.

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