Number and Operations>Determining the Constant of Proportionality (k = y/x)(TEKS.Math.7.4.C)
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Texas 7th Grade Math › Number and Operations>Determining the Constant of Proportionality (k = y/x)(TEKS.Math.7.4.C)
The relationship between hours worked (x) and pay (y) is represented by the ordered pairs: (2, 26), (5, 65), (8, 104). What is the constant of proportionality $k$ in $y=kx$?
45670
5
13
8
Explanation
The constant of proportionality is the consistent ratio $k=\dfrac{y}{x}$. Using (2, 26): $26/2=13$; using (5, 65): $65/5=13$; using (8, 104): $104/8=13$. So $k=13$, the unit rate (slope) of dollars per hour.
When $x$-values are 4, 6, 8, the corresponding $y$-values are 12, 18, 24. What is the value of $k$ in $y=kx$?
3
45660
2
4
Explanation
In a proportional relationship, $k=\dfrac{y}{x}$. Compute: $12/4=3$, $18/6=3$, and $24/8=3$. The ratio $y/x$ is the same for all pairs, so $k=3$ (the unit rate/slope).
A recipe relates batches baked ($x$) to cups of flour used ($y$) with these pairs: (1, 3), (3, 9), (4, 12). What is the constant of proportionality $k$ in $y=kx$?
12
2
45660
3
Explanation
The constant of proportionality is $k=\dfrac{y}{x}$. Using (1, 3): $3/1=3$; using (3, 9): $9/3=3$; using (4, 12): $12/4=3$. The ratio $y/x$ is consistent, so $k=3$ cups per batch (the unit rate/slope).
The relationship is proportional with $x$-values 2.5, 4, 6.5 and $y$-values 5, 8, 13. What is the value of $k$ in $y=kx$?
1
2
8/6.5
1
Explanation
Compute $k=\dfrac{y}{x}$ for any pair: $5/2.5=2$, $8/4=2$, $13/6.5=2$. Because $y/x$ is the same for all pairs, $k=2$ (the unit rate/slope). Distractors use $x/y$ or mix nonmatching values.
A bike rental charges a constant rate. Hours rented ($x$) and total cost ($y$) are: (1.5, 12), (2.75, 22), (4, 32). What is the constant of proportionality $k$ in $y=kx$?
8
45665
6
0
Explanation
Since the relationship is proportional, $k=\dfrac{y}{x}$. Using (1.5, 12): $12/1.5=8$; using (2.75, 22): $22/2.75=8$; using (4, 32): $32/4=8$. The consistent ratio $y/x$ shows $k=8$ (the unit rate/slope).