Identify Constant of Proportionality - 7th Grade Math
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What is the constant of proportionality $k$ in the equation $y = 0.6x$?
What is the constant of proportionality $k$ in the equation $y = 0.6x$?
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$k = 0.6$. The constant $k$ is the coefficient of $x$ in the equation.
$k = 0.6$. The constant $k$ is the coefficient of $x$ in the equation.
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Which value is the constant of proportionality for $y = kx$ if the relationship includes the point $(7, -28)$?
Which value is the constant of proportionality for $y = kx$ if the relationship includes the point $(7, -28)$?
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$k = -4$. Solve for $k$: $-28 = k(7)$, so $k = \frac{-28}{7} = -4$.
$k = -4$. Solve for $k$: $-28 = k(7)$, so $k = \frac{-28}{7} = -4$.
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What is the constant of proportionality $k$ if $y$ is proportional to $x$ and $y$ increases by $8$ when $x$ increases by $2$?
What is the constant of proportionality $k$ if $y$ is proportional to $x$ and $y$ increases by $8$ when $x$ increases by $2$?
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$k = \frac{8}{2} = 4$. Rate of change = $\frac{\Delta y}{\Delta x} = \frac{8}{2} = 4$.
$k = \frac{8}{2} = 4$. Rate of change = $\frac{\Delta y}{\Delta x} = \frac{8}{2} = 4$.
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Identify $k$ if $\$45$ buys $6$ tickets and total cost is proportional to number of tickets.
Identify $k$ if $\$45$ buys $6$ tickets and total cost is proportional to number of tickets.
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$k = \$7.50$ per ticket. Price per ticket = $\frac{45}{6} = 7.50$ dollars.
$k = \$7.50$ per ticket. Price per ticket = $\frac{45}{6} = 7.50$ dollars.
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What is the unit rate $k$ if $12$ apples cost $\$18$ and cost is proportional to number of apples?
What is the unit rate $k$ if $12$ apples cost $\$18$ and cost is proportional to number of apples?
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$k = \$1.50$ per apple. Unit price = $\frac{\text{total cost}}{\text{quantity}} = \frac{18}{12} = 1.50$.
$k = \$1.50$ per apple. Unit price = $\frac{\text{total cost}}{\text{quantity}} = \frac{18}{12} = 1.50$.
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What is the unit rate (constant of proportionality) if a car travels $180$ miles in $3$ hours at a constant speed?
What is the unit rate (constant of proportionality) if a car travels $180$ miles in $3$ hours at a constant speed?
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$k = 60$ miles per hour. Unit rate = $\frac{\text{distance}}{\text{time}} = \frac{180}{3} = 60$ mph.
$k = 60$ miles per hour. Unit rate = $\frac{\text{distance}}{\text{time}} = \frac{180}{3} = 60$ mph.
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Identify $k$ in this table: $(x,y)=(2,3),(6,9),(10,15)$ for $y = kx$.
Identify $k$ in this table: $(x,y)=(2,3),(6,9),(10,15)$ for $y = kx$.
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$k = \frac{3}{2}$. For each pair, $\frac{y}{x} = \frac{3}{2}$.
$k = \frac{3}{2}$. For each pair, $\frac{y}{x} = \frac{3}{2}$.
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Identify the constant of proportionality $k$ in this table: $(x,y)=(1,7),(2,14),(3,21)$.
Identify the constant of proportionality $k$ in this table: $(x,y)=(1,7),(2,14),(3,21)$.
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$k = 7$. Each $y$-value divided by its $x$-value equals $7$.
$k = 7$. Each $y$-value divided by its $x$-value equals $7$.
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What is the constant of proportionality $k$ for a line through $(0, 0)$ and $(10, 4)$ in $y = kx$?
What is the constant of proportionality $k$ for a line through $(0, 0)$ and $(10, 4)$ in $y = kx$?
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$k = \frac{4}{10} = \frac{2}{5}$. Calculate $k = \frac{y}{x} = \frac{4}{10} = \frac{2}{5}$.
$k = \frac{4}{10} = \frac{2}{5}$. Calculate $k = \frac{y}{x} = \frac{4}{10} = \frac{2}{5}$.
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What is the constant of proportionality $k$ for a graph of $y = kx$ that passes through $(0, 0)$ and $(3, 9)$?
What is the constant of proportionality $k$ for a graph of $y = kx$ that passes through $(0, 0)$ and $(3, 9)$?
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$k = 3$. Use the non-origin point: $k = \frac{9}{3} = 3$.
$k = 3$. Use the non-origin point: $k = \frac{9}{3} = 3$.
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Identify $k$ in a proportional table where the pair is $(x, y) = (5, -20)$ and $y = kx$.
Identify $k$ in a proportional table where the pair is $(x, y) = (5, -20)$ and $y = kx$.
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$k = -4$. Calculate $k = \frac{y}{x} = \frac{-20}{5} = -4$.
$k = -4$. Calculate $k = \frac{y}{x} = \frac{-20}{5} = -4$.
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What is the constant of proportionality $k$ in the table where $x = 2$ gives $y = 11$ and $y = kx$?
What is the constant of proportionality $k$ in the table where $x = 2$ gives $y = 11$ and $y = kx$?
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$k = \frac{11}{2}$. Divide $y$ by $x$ to find $k$: $k = \frac{11}{2}$.
$k = \frac{11}{2}$. Divide $y$ by $x$ to find $k$: $k = \frac{11}{2}$.
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Identify the unit rate $k$ if $x = 9$ corresponds to $y = 12$ in a proportional relationship $y = kx$.
Identify the unit rate $k$ if $x = 9$ corresponds to $y = 12$ in a proportional relationship $y = kx$.
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$k = \frac{12}{9} = \frac{4}{3}$. The unit rate is $k = \frac{y}{x} = \frac{12}{9} = \frac{4}{3}$.
$k = \frac{12}{9} = \frac{4}{3}$. The unit rate is $k = \frac{y}{x} = \frac{12}{9} = \frac{4}{3}$.
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Identify $k$ if $y$ is proportional to $x$ and the point $(4, 14)$ is on the graph of $y = kx$.
Identify $k$ if $y$ is proportional to $x$ and the point $(4, 14)$ is on the graph of $y = kx$.
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$k = \frac{14}{4} = \frac{7}{2}$. Substitute the point into $y = kx$: $14 = k(4)$, so $k = \frac{14}{4}$.
$k = \frac{14}{4} = \frac{7}{2}$. Substitute the point into $y = kx$: $14 = k(4)$, so $k = \frac{14}{4}$.
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Identify $k$ for the proportional relationship $y$ varies directly with $x$ and $y = 18$ when $x = 6$.
Identify $k$ for the proportional relationship $y$ varies directly with $x$ and $y = 18$ when $x = 6$.
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$k = 3$. Find $k$ by dividing: $k = \frac{y}{x} = \frac{18}{6} = 3$.
$k = 3$. Find $k$ by dividing: $k = \frac{y}{x} = \frac{18}{6} = 3$.
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What is the constant of proportionality $k$ in the equation $y = \frac{x}{8}$?
What is the constant of proportionality $k$ in the equation $y = \frac{x}{8}$?
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$k = \frac{1}{8}$. Rewrite as $y = \frac{1}{8}x$ to identify $k = \frac{1}{8}$.
$k = \frac{1}{8}$. Rewrite as $y = \frac{1}{8}x$ to identify $k = \frac{1}{8}$.
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What is the constant of proportionality $k$ in the equation $y = -2x$?
What is the constant of proportionality $k$ in the equation $y = -2x$?
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$k = -2$. In $y = kx$, $k$ is the coefficient multiplying $x$.
$k = -2$. In $y = kx$, $k$ is the coefficient multiplying $x$.
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What is the constant of proportionality $k$ in the equation $y = \frac{3}{4}x$?
What is the constant of proportionality $k$ in the equation $y = \frac{3}{4}x$?
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$k = \frac{3}{4}$. The coefficient of $x$ in $y = kx$ form is the constant $k$.
$k = \frac{3}{4}$. The coefficient of $x$ in $y = kx$ form is the constant $k$.
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What is the constant of proportionality $k$ in the equation $y = 5x$?
What is the constant of proportionality $k$ in the equation $y = 5x$?
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$k = 5$. In $y = kx$, the coefficient of $x$ is the constant of proportionality.
$k = 5$. In $y = kx$, the coefficient of $x$ is the constant of proportionality.
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On a graph of a proportional relationship $y = kx$, what does the constant $k$ represent?
On a graph of a proportional relationship $y = kx$, what does the constant $k$ represent?
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$k$ is the slope (rise per $1$ unit run)
$k$ is the slope (rise per $1$ unit run)
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What is the formula for the constant of proportionality in $y = kx$ using any nonzero point $(x,y)$?
What is the formula for the constant of proportionality in $y = kx$ using any nonzero point $(x,y)$?
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$k = \frac{y}{x}$
$k = \frac{y}{x}$
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What must be true about the point $(0,0)$ on the graph if a relationship is proportional?
What must be true about the point $(0,0)$ on the graph if a relationship is proportional?
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The graph must pass through $(0,0)$
The graph must pass through $(0,0)$
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Which expression gives the constant of proportionality for a proportional table of $x$ and $y$ values?
Which expression gives the constant of proportionality for a proportional table of $x$ and $y$ values?
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$k = \frac{y}{x}$. For proportional relationships, $k$ equals $y$ divided by $x$.
$k = \frac{y}{x}$. For proportional relationships, $k$ equals $y$ divided by $x$.
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Identify the unit rate $k$ if $\frac{5}{6}$ pound of cheese costs $\$4$.
Identify the unit rate $k$ if $\frac{5}{6}$ pound of cheese costs $\$4$.
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$k = \frac{4}{\frac{5}{6}} = \frac{24}{5} = 4.8$ dollars per pound. Divide price by weight to find dollars per pound.
$k = \frac{4}{\frac{5}{6}} = \frac{24}{5} = 4.8$ dollars per pound. Divide price by weight to find dollars per pound.
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Identify the unit rate $k$ if a recipe uses $\frac{3}{4}$ cup of sugar for $2$ batches.
Identify the unit rate $k$ if a recipe uses $\frac{3}{4}$ cup of sugar for $2$ batches.
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$k = \frac{\frac{3}{4}}{2} = \frac{3}{8}$ cup per batch. Divide amount of sugar by number of batches for sugar per batch.
$k = \frac{\frac{3}{4}}{2} = \frac{3}{8}$ cup per batch. Divide amount of sugar by number of batches for sugar per batch.
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