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

Answer:

No, Sam is not correct. The graph of a proportional relationship has the form y = kx, where k is the constant of proportionality. Sam added the constant of proportionality instead of using it as the coefficient of x. The correct equation is y = 6x. Sam’s graph would be a straight line, but it would not pass through the origin.

Answer 2

No, the equation written by Sam isn't correct.

• When two variables are proportional to each other, it refers to the change in one that will bring a change in the other. For example, increasing the distance travelled and keeping the time constant increases the speed.

• To eliminate the sign of proportionality, we multiply the variable by some constant, also known as the constant of proportionality.

• In the given question, the equation in its raw form is y = kx. Substituting the proportionality constant, we obtain y = 6x. Whereas, in Sam's equation, 6 is not the proportionality constant.