The equation y = 1/5 x represents a proportional relationship. Explain how you can tell the relationship is proportional from the graph of the equation, and how you can find the constant of proportionality.

the answer is i got it! When you graph the equation, you get a straight line that passes through the origin, which means the relationship is proportional. The constant of proportionality is the y-value when x = 1, which is 15.

Question

Mathematics

Tiggy

29 January, 08:12

The equation y = 1/5 x represents a proportional relationship. Explain how you can tell the relationship is proportional from the graph of the equation, and how you can find the constant of proportionality.

the answer is i got it! When you graph the equation, you get a straight line that passes through the origin, which means the relationship is proportional. The constant of proportionality is the y-value when x = 1, which is 15.

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Answers (1)

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Martha Grimes · Answer 1

An equation of the form y=ax+b, where y and x are variables, and a and b are constants, is called a linear equation.

The reason it is called linear is because the graph of the equation is a line.

The line passes through the origin only if b=0, as in our problem.

Any line (except vertical lines) represents a proportional relationship in that the change in y is proportional with the change in x. It is not a condition that the line passes through the origin.

In our specific case, y = (1/5) x, means that the change in y is always 1/5 of the change in x. That is, if x changes by 5 units, y changes by 1. If x changes by 10 units, y changes by 2, and so on.

So, the constant of proportionality is 1:5, or 0.2.