Suppose y is directly proportinal to x

[mech-eng]

Homework Statement

[/B]

Suppose that y is directly proportional to x. Show that y is a linear function of x. Both lines goes through the origin. First line goes 1250 ft in x direction and 50 ft in y direction. The second line goes 13740 ft in x direction and 920.58 ft in y direction.

Source: Algebra and Trigonometry by Keedy/Bittinger.

Homework Equations

y=mx+n[/B]

The Attempt at a Solution

1.y=mx+n since line goes through the origin y-intercept is 0. We know y-intercept and slope then we can write a slope-intercept equation for the line. m=50/1250=0.04; y=0.04x

2. y=mx+n since line goes through the origin y-intercept is 0. We know y-intercept and slope then we can write a slope-intercept equation for the line. m=0.067x

But here I do not understand why the information "y is directly proportional to x" is given? What are other ways to solve this problem?

Thank you.

[/B]

 

[Arman777]

But here I do not understand why the information "y is directly proportional to x" is given? What are other ways to solve this problem?

Its given cause its implies x is proportional to y. Like y=ax where a is a constant reel number this function like y=ax so f(x)=ax is a linear function.I don't think there's any other way to solve this question.

 

[mech-eng]

Isn't y in y=x²directly proportinal to x?

 

[Arman777]

Isn't y in y=x²directly proportinal to x?

Its not

 

[DrClaude]

If y is directly proportional to x, then doubling the value of x doubles the value of y.

 

[mech-eng]

If y is directly proportional to x, then doubling the value of x doubles the value of y.

How is this square case of proportionality called?

Thank you.

 

[DrClaude]

How is this square case of proportionality called?

"y is proportional to x squared"

Mathematically, it is the difference between $y \propto x$ and $y \propto x^2$.

 

[Ray Vickson]

How is this square case of proportionality called?

Thank you.

$y$ proportional to $f(x)$ just means that $y/f(x)$ is a constant; that is, $y = c f(x)$ for some constant $c$.

 

[CWatters]

What's with the question numbers (50,51,52)? Is 50 referring to 51 and 52?

 

[mech-eng]

What's with the question numbers (50,51,52)? Is 50 referring to 51 and 52?

I think 50 is the question and 51 and 52 are parts of it. That's all in the picture.

Thank you.