Question

use the coordinates to answer the following questions.

x

y

(x,y)

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----

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0

$\frac{1}{3}$

$(0, \frac{1}{3})$

$\frac{2}{3}$

1

$(\frac{2}{3},1)$

1

$1\frac{1}{3}$

$(1,1\frac{1}{3})$

is more than less than 1 y $\frac{1}{3}$ x

Explanation:

Step1: Find slope from points

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$. Take $(0,\frac{1}{3})$ and $(\frac{2}{3},1)$:
$m=\frac{1-\frac{1}{3}}{\frac{2}{3}-0}=\frac{\frac{2}{3}}{\frac{2}{3}}=1$

Step2: Write linear equation

Use slope-intercept form $y=mx+b$. $b=\frac{1}{3}$, $m=1$:
$y = x + \frac{1}{3}$

Step3: Rearrange to compare y and x

Rewrite the equation to isolate the relationship:
$y - x = \frac{1}{3}$, so $y$ is more than $x$ by $\frac{1}{3}$

Answer:

$y$ is more than $x$ by $\frac{1}{3}$ (or the completed statement: $y$ is more than $x$)