# Homework Help: Suppose y is directly proportinal to x

1. May 5, 2017

### mech-eng

1. The problem statement, all variables and given/known data

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.
2. Relevant equations
y=mx+n

3. 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.

2. May 5, 2017

### Arman777

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 dont think theres any other way to solve this question.

3. May 5, 2017

### mech-eng

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

4. May 5, 2017

Its not

5. May 5, 2017

### Staff: Mentor

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

6. May 5, 2017

### mech-eng

How is this square case of proportionality called?

Thank you.

7. May 5, 2017

### Staff: Mentor

"y is proportional to x squared"

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

8. May 5, 2017

### Ray Vickson

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

9. May 5, 2017

### CWatters

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

10. May 5, 2017

### mech-eng

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

Thank you.