Question

roy is hooked on a new book series, the galaxy. each book in the series is the same length and chronicles a different year in the waka waka galaxy. roy has cleared off the top shelf of his bookcase to leave room for each of the books as they come out. there is a proportional relationship between the number of books on the shelf, x, and how much shelf space the books take up (in inches), y. chart: x-axis (books) from 0 to 10, y-axis (inches) from 0 to 10, line through origin with slope, e.g., (2,4), (5,10). write an equation for the relationship between x and y. simplify any fractions. y = \boxed{}

Explanation:

Step1: Identify proportional form

Proportional relationships follow $y=kx$, where $k$ is the constant of proportionality.

Step2: Find k from graph

Pick a point on the line, e.g., $(5,10)$. Calculate $k=\frac{y}{x}$.
$\frac{10}{5}=2$

Step3: Write the equation

Substitute $k=2$ into $y=kx$.
$y=2x$

Answer:

$y=2x$