Question

Sam wants to write an equation to represent a proportional relationship with a constant of proportionality of 6. He writes the equation y = 6 + x.

Is he correct. If not, what is the correct equation? Explain your answer. Consider the graph of the equation in your response

Answer 1

No — Sam is not correct.

A proportional relationship between y and x with constant of proportionality 6 means y = 6x (the constant multiplies x). Sam's equation y = 6 + x is not proportional because it adds 6 instead of multiplying.

Graphically:
- y = 6x is a straight line through the origin (0,0) with slope 6. Every point satisfies y/x = 6 (e.g. (1,6), (2,12)).
- y = x + 6 is a straight line with slope 1 and y-intercept 6; it does not pass through the origin (e.g. (0,6), (1,7)). The ratio y/x is not constant there (7/1 = 7, 8/2 = 4), so it's not a proportional relationship.

Therefore the correct equation is y = 6x.