Proportional Relationships - SSAT Middle Level: Quantitative
Card 1 of 23
What equation solves a proportional relationship if you know $k$ and $x$?
What equation solves a proportional relationship if you know $k$ and $x$?
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$y = kx$. This equation expresses y as the product of the constant of proportionality and x.
$y = kx$. This equation expresses y as the product of the constant of proportionality and x.
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What equation solves a proportional relationship if you know $k$ and $y$?
What equation solves a proportional relationship if you know $k$ and $y$?
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$x = \frac{y}{k}$. Rearranging the proportional equation isolates x by dividing y by the constant k.
$x = \frac{y}{k}$. Rearranging the proportional equation isolates x by dividing y by the constant k.
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What is the cross-multiplication setup for solving $\frac{a}{b} = \frac{c}{d}$?
What is the cross-multiplication setup for solving $\frac{a}{b} = \frac{c}{d}$?
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$ad = bc$. Cross-multiplication equates the product of one fraction's numerator and the other's denominator.
$ad = bc$. Cross-multiplication equates the product of one fraction's numerator and the other's denominator.
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Identify the missing value $y$: $\frac{y}{8} = \frac{3}{4}$.
Identify the missing value $y$: $\frac{y}{8} = \frac{3}{4}$.
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$y = 6$. Cross-multiplying or scaling the right side by 8 yields the value of y.
$y = 6$. Cross-multiplying or scaling the right side by 8 yields the value of y.
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Identify the missing value $x$: $\frac{5}{x} = \frac{15}{12}$.
Identify the missing value $x$: $\frac{5}{x} = \frac{15}{12}$.
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$x = 4$. Cross-multiplying the proportion solves for the unknown denominator x.
$x = 4$. Cross-multiplying the proportion solves for the unknown denominator x.
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What is $k$ if a table includes the pair $(x,y) = (6,15)$ and is proportional?
What is $k$ if a table includes the pair $(x,y) = (6,15)$ and is proportional?
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$k = \frac{15}{6} = \frac{5}{2}$. The constant k is determined by dividing y by x from the given proportional pair.
$k = \frac{15}{6} = \frac{5}{2}$. The constant k is determined by dividing y by x from the given proportional pair.
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What is $y$ if $y$ is proportional to $x$ with $k = 7$ and $x = 3$?
What is $y$ if $y$ is proportional to $x$ with $k = 7$ and $x = 3$?
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$y = 21$. Substitute the given k and x into the proportional equation y = kx.
$y = 21$. Substitute the given k and x into the proportional equation y = kx.
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What is $x$ if $y$ is proportional to $x$ with $k = 4$ and $y = 52$?
What is $x$ if $y$ is proportional to $x$ with $k = 4$ and $y = 52$?
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$x = 13$. Rearrange the proportional equation to solve for x by dividing y by k.
$x = 13$. Rearrange the proportional equation to solve for x by dividing y by k.
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Identify $k$ in the proportional equation $y = \frac{3}{5}x$.
Identify $k$ in the proportional equation $y = \frac{3}{5}x$.
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$k = \frac{3}{5}$. The constant k is the coefficient multiplying x in the given equation.
$k = \frac{3}{5}$. The constant k is the coefficient multiplying x in the given equation.
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Find $y$ if $y = \frac{3}{5}x$ and $x = 20$.
Find $y$ if $y = \frac{3}{5}x$ and $x = 20$.
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$y = 12$. Multiply the given x by the constant ratio to find y.
$y = 12$. Multiply the given x by the constant ratio to find y.
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Find $x$ if $y = \frac{3}{5}x$ and $y = 18$.
Find $x$ if $y = \frac{3}{5}x$ and $y = 18$.
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$x = 30$. Divide y by the constant ratio or multiply by its reciprocal to solve for x.
$x = 30$. Divide y by the constant ratio or multiply by its reciprocal to solve for x.
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Which value of $k$ makes $y$ proportional to $x$ if $(x,y) = (9,6)$?
Which value of $k$ makes $y$ proportional to $x$ if $(x,y) = (9,6)$?
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$k = \frac{6}{9} = \frac{2}{3}$. k is the reduced fraction of y divided by x from the provided pair.
$k = \frac{6}{9} = \frac{2}{3}$. k is the reduced fraction of y divided by x from the provided pair.
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Identify the missing value $y$: $\frac{y}{14} = \frac{5}{7}$.
Identify the missing value $y$: $\frac{y}{14} = \frac{5}{7}$.
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$y = 10$. Solve the proportion by cross-multiplying or scaling the numerator.
$y = 10$. Solve the proportion by cross-multiplying or scaling the numerator.
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Find $y$ if $y$ is proportional to $x$ and $\frac{y}{x} = \frac{7}{9}$ with $x = 27$.
Find $y$ if $y$ is proportional to $x$ and $\frac{y}{x} = \frac{7}{9}$ with $x = 27$.
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$y = 21$. Multiply the given x by the constant ratio to determine y.
$y = 21$. Multiply the given x by the constant ratio to determine y.
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Find $x$ if $y$ is proportional to $x$ and $\frac{y}{x} = \frac{7}{9}$ with $y = 28$.
Find $x$ if $y$ is proportional to $x$ and $\frac{y}{x} = \frac{7}{9}$ with $y = 28$.
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$x = 36$. Divide y by the ratio or multiply by its reciprocal to find x.
$x = 36$. Divide y by the ratio or multiply by its reciprocal to find x.
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Find $y$ if the proportional equation is $y = \frac{5}{2}x$ and $x = 6$.
Find $y$ if the proportional equation is $y = \frac{5}{2}x$ and $x = 6$.
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$y = 15$. Substitute the given x into the equation to compute y.
$y = 15$. Substitute the given x into the equation to compute y.
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What is the missing value $y$ in the proportion $\frac{9}{12} = \frac{y}{20}$?
What is the missing value $y$ in the proportion $\frac{9}{12} = \frac{y}{20}$?
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$y = 15$. Cross-multiply or simplify the left ratio and scale to solve for y.
$y = 15$. Cross-multiply or simplify the left ratio and scale to solve for y.
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Is the table proportional if $(x,y)$ includes $(2,6)$ and $(5,15)$? Answer yes or no.
Is the table proportional if $(x,y)$ includes $(2,6)$ and $(5,15)$? Answer yes or no.
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Yes, because $\frac{6}{2} = \frac{15}{5} = 3$. Equal ratios of y to x for both pairs indicate a constant of proportionality.
Yes, because $\frac{6}{2} = \frac{15}{5} = 3$. Equal ratios of y to x for both pairs indicate a constant of proportionality.
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Identify the missing value $x$: $\frac{12}{x} = \frac{3}{8}$.
Identify the missing value $x$: $\frac{12}{x} = \frac{3}{8}$.
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$x = 32$. Cross-multiplying the proportion isolates and solves for x.
$x = 32$. Cross-multiplying the proportion isolates and solves for x.
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What is the equation of a proportional relationship through $(0,0)$ and $(4,10)$?
What is the equation of a proportional relationship through $(0,0)$ and $(4,10)$?
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$y = \frac{5}{2}x$. The line through origin and the point has slope k equal to y/x.
$y = \frac{5}{2}x$. The line through origin and the point has slope k equal to y/x.
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Is the table proportional if $(x,y)$ includes $(3,8)$ and $(6,15)$? Answer yes or no.
Is the table proportional if $(x,y)$ includes $(3,8)$ and $(6,15)$? Answer yes or no.
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No, because $\frac{8}{3} \ne \frac{15}{6}$. Unequal ratios of y to x show the relationship is not proportional.
No, because $\frac{8}{3} \ne \frac{15}{6}$. Unequal ratios of y to x show the relationship is not proportional.
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What does it mean for two quantities $x$ and $y$ to be proportional?
What does it mean for two quantities $x$ and $y$ to be proportional?
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$\frac{y}{x}$ is constant (equivalently, $y = kx$ for some constant $k$). Proportional quantities maintain a constant ratio, allowing representation as y equaling a constant multiple of x.
$\frac{y}{x}$ is constant (equivalently, $y = kx$ for some constant $k$). Proportional quantities maintain a constant ratio, allowing representation as y equaling a constant multiple of x.
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What is the constant of proportionality $k$ in the equation $y = kx$?
What is the constant of proportionality $k$ in the equation $y = kx$?
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$k = \frac{y}{x}$ (for any pair with $x \ne 0$). The constant k represents the fixed ratio of y to x in any corresponding pair of values.
$k = \frac{y}{x}$ (for any pair with $x \ne 0$). The constant k represents the fixed ratio of y to x in any corresponding pair of values.
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