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Read the description of a proportional relationship. $\newline$ Tanner has outgrown the bike he rode when he was small. So, for his twelfth birthday, his parents surprise him with a five-speed Blaze Rider $2000$ ! Tanner has never had a bike with multiple speeds before, and he is eager to learn how it works. He starts by testing the middle speed. There is a proportional relationship between the number of times Tanner pedals, $x$ , and the number of times the wheels rotate, $y$ . $\newline$ When he pedals $4$ times, the wheels rotate $8$ times. Write the equation for the relationship between $x$ and $y$ . $\newline$ $y = \_\_$

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Write and solve equations for proportional relationships

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Q. Read the description of a proportional relationship.

\newline

Tanner has outgrown the bike he rode when he was small. So, for his twelfth birthday, his parents surprise him with a five-speed Blaze Rider

2000

! Tanner has never had a bike with multiple speeds before, and he is eager to learn how it works. He starts by testing the middle speed. There is a proportional relationship between the number of times Tanner pedals,

x

, and the number of times the wheels rotate,

y

.

\newline

When he pedals

4

times, the wheels rotate

8

times. Write the equation for the relationship between

x

and

y

.

\newline

y = \_\_

Identify Given Values: Step $1$ : Identify the given values from the problem description. $\newline$ Tanner pedals $4$ times ( $x = 4$ ) and the wheels rotate $8$ times ( $y = 8$ ). $\newline$ Calculate the constant of proportionality, $k$ . $\newline$ $k = \frac{y}{x} = \frac{8}{4} = 2$
Calculate Constant: Step $2$ : Write the equation for the proportional relationship using the constant of proportionality. $\newline$ Since $k = 2$ , the equation is $y = kx$ . $\newline$ Therefore, $y = 2x$

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