Question

solve.
5 plot a point for the ordered pairs (from the example problem) shown at the right. model the relationships by drawing a line from the y - axis through each point. explain how the graphs show which relationship is proportional and which is not proportional.

6 determine whether each equation below does or does not represent a proportional relationship. support your answer using either a table or a graph.
equation a: ( y = x )
equation b: ( y = x + 2 )
7 zahra has paper rectangles of different sizes. every rectangle is 5 centimeters longer than it is wide. is there a proportional relationship between the lengths and widths of these rectangles? explain.

Explanation:

Step1: Analyze Equation A ($y = x$)

A proportional relationship has the form $y=kx$ where $k$ is the constant of proportionality. For $y = x$, $k = 1$. When $x = 0$, $y=0$. We can create a table:

$x$	$y$	$\frac{y}{x}$
$2$	$2$	$1$
$3$	$3$	$1$

The ratio $\frac{y}{x}$ is constant.

Step2: Analyze Equation B ($y=x + 2$)

For a proportional relationship, when $x = 0$, $y$ must be $0$. For $y=x + 2$, when $x=0$, $y = 2
eq0$. Create a table:

$x$	$y$	$\frac{y}{x}$
$2$	$4$	$2$
$3$	$5$	$\frac{5}{3}$

The ratio $\frac{y}{x}$ is not constant.

Answer:

Equation A ($y = x$) represents a proportional relationship because it can be written as $y=kx$ ($k = 1$) and the ratio $\frac{y}{x}$ is constant. Equation B ($y=x + 2$) does not represent a proportional relationship because when $x = 0$, $y
eq0$ and the ratio $\frac{y}{x}$ is not constant.