need help with wording: "The variable y is __ [for their example they said directly]

[rositahill]

need help with wording: "The variable y is __ [for their example they said directly]

So I have a problem with figuring out how to word a sentence for a plain linear expression that has a y intercept.

The format they gave us is "The variable y is _______ [for their example they said directly] proportional to the variable x, with a constant of proportionality of 8."

The equation given is not directly proportional because it has a y-intercept so it is just linear, putting it as linearly proportional doesn't sound right to me though.

 

[Deleted member 4993]

So I have a problem with figuring out how to word a sentence for a plain linear expression that has a y intercept.

The format they gave us is "The variable y is _______ [for their example they said directly] proportional to the variable x, with a constant of proportionality of 8."

The equation given is not directly proportional because it has a y-intercept so it is just linear, putting it as linearly proportional doesn't sound right to me though.

This may not be what your instructor wants, but to me:

y = mx + b → (y-b) = mx → "The variable (y-b) is directly proportional to the variable x, with a constant of proportionality of m."

 

[Ishuda]

So I have a problem with figuring out how to word a sentence for a plain linear expression that has a y intercept.

The format they gave us is "The variable y is _______ [for their example they said directly] proportional to the variable x, with a constant of proportionality of 8."

The equation given is not directly proportional because it has a y-intercept so it is just linear, putting it as linearly proportional doesn't sound right to me though.

A generally accepted definition of being directly proportional is that the ratio of the two items are constant so that if A is directly proportional to B then A divided by B is constant, i.e.
A/B = k
where k is some constant. Or, so that we can take care of the case B=0,
A = k * B

So, as Subhotosh Khan implied, 'y is directly proportional to x' just means that the y intercept of a linear equation is zero and that the slope is the constant of proportionality.