Question

16. In a proportional relationship, why must the graph of the line always go through the origin (0,0)? Hint: Use your cost equations to help you answer this question.

Answer 1

We know that,

A proportional relationship is the relation in which two quantities varies directly with each other.

i.e. x and y are said to be proportional if they are of the form 'y=kx' where k is any constant called the constant of proportionality.

Now, as we have the equation y = kx.

So, we will substitute the value x = 0 in the equation.

i.e. y = kx ⇒ y = k × 0 ⇒ y = 0.

Thus, we get that the point (0,0) satisfies the relation for proportionality i.e. it is a solution of y = kx.

Hence, the graph of y=kx will pass through (0,0) i.e. the graph of proportionality will pass through (0,0).