Question

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1. a proportional relationship is modeled by the equation $y = \frac{1}{2}x$. complete the table, graph the relationship and give the constant of proportionality.\

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input $x$	output $y$	\
---	---	\
0		\
1		\
2		\
3		\
4		\

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unit rate: \
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find the slope of each line and write in the slope in simplest form.\

1. \

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slope: \

1. \

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slope: \

1. \

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slope: \

1. both tyson and jamaal work after - school jobs. the table below shows the amount of money jamaal earned at his job based on the number of hours worked. tyson calculates his earnings ($p$) based on the number of hours ($h$) he works using the equation $p = 8.9h$. who makes the most money per hour? what is the difference between tyson and jamaal’s hourly wage?\

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hours tutoring	money earned ($)	\
---	---	\
0	0	\
4	38.00	\
8	76.00	\
12	114.00	\
16	152.00

Explanation:

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Problem 6

Step1: Substitute x=0 into equation

$y=\frac{1}{2}(0)=0$

Step2: Substitute x=1 into equation

$y=\frac{1}{2}(1)=\frac{1}{2}$

Step3: Substitute x=2 into equation

$y=\frac{1}{2}(2)=1$

Step4: Substitute x=3 into equation

$y=\frac{1}{2}(3)=\frac{3}{2}$

Step5: Substitute x=4 into equation

$y=\frac{1}{2}(4)=2$

Step6: Identify proportionality constant

For $y=kx$, $k=\frac{1}{2}$

Step1: Pick two points on the line

Use $(0,0)$ and $(2,6)$

Step2: Apply slope formula $m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{6-0}{2-0}=\frac{6}{2}=3$

Step1: Pick two points on the line

Use $(-4,-6)$ and $(2,-6)$

Step2: Apply slope formula $m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{-6-(-6)}{2-(-4)}=\frac{0}{6}=0$

Answer:

Input $x$	Output $y$
1	$\frac{1}{2}$
2	1
3	$\frac{3}{2}$
4	2

Unit Rate (Constant of Proportionality): $\frac{1}{2}$
(Graph: Plot points (0,0), (1, 0.5), (2,1), (3,1.5), (4,2) and draw a straight line through them)

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Problem 7