Represent Proportional Relationships by Equations - 7th Grade Math
Card 1 of 25
Find $n$ if $t = 45$, $p = 9$, and $t = pn$.
Find $n$ if $t = 45$, $p = 9$, and $t = pn$.
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$n = 5$. Solve $45 = 9n$ by dividing both sides by $9$.
$n = 5$. Solve $45 = 9n$ by dividing both sides by $9$.
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Identify $k$ in the equation $y = \frac{2}{3}x$.
Identify $k$ in the equation $y = \frac{2}{3}x$.
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$k = \frac{2}{3}$. The coefficient of $x$ is the constant of proportionality.
$k = \frac{2}{3}$. The coefficient of $x$ is the constant of proportionality.
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Find $t$ if $t = 4n$ and $n = 7$.
Find $t$ if $t = 4n$ and $n = 7$.
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$t = 28$. Substitute $n = 7$ into $t = 4n$: $t = 4(7) = 28$.
$t = 28$. Substitute $n = 7$ into $t = 4n$: $t = 4(7) = 28$.
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Write an equation for total cost $t$ when price per item is $p = \frac{5}{2}$ and number of items is $n$.
Write an equation for total cost $t$ when price per item is $p = \frac{5}{2}$ and number of items is $n$.
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$t = \frac{5}{2}n$. Substitute $p = \frac{5}{2}$ into the formula $t = pn$.
$t = \frac{5}{2}n$. Substitute $p = \frac{5}{2}$ into the formula $t = pn$.
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Write an equation for total cost $t$ when price per item is $p = 6$ dollars and number of items is $n$.
Write an equation for total cost $t$ when price per item is $p = 6$ dollars and number of items is $n$.
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$t = 6n$. Substitute $p = 6$ into the formula $t = pn$.
$t = 6n$. Substitute $p = 6$ into the formula $t = pn$.
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What is the equation for distance $d$ proportional to time $t$ at speed $v$?
What is the equation for distance $d$ proportional to time $t$ at speed $v$?
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$d = vt$. Distance equals rate times time in proportional motion.
$d = vt$. Distance equals rate times time in proportional motion.
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Identify the error: “$y = k + x$ represents a proportional relationship.” What is the correct form?
Identify the error: “$y = k + x$ represents a proportional relationship.” What is the correct form?
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Correct form: $y = kx$. Proportional relationships have no constant term, only $y = kx$.
Correct form: $y = kx$. Proportional relationships have no constant term, only $y = kx$.
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What is the constant of proportionality $k$ if a point $(x,y) = (5,20)$ is on $y = kx$?
What is the constant of proportionality $k$ if a point $(x,y) = (5,20)$ is on $y = kx$?
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$k = 4$. Substitute $(5,20)$ into $y = kx$: $20 = k(5)$, so $k = 4$.
$k = 4$. Substitute $(5,20)$ into $y = kx$: $20 = k(5)$, so $k = 4$.
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Which equation shows a proportional relationship: $y = 3x$ or $y = 3x + 2$?
Which equation shows a proportional relationship: $y = 3x$ or $y = 3x + 2$?
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$y = 3x$. Only $y = 3x$ passes through origin; $y = 3x + 2$ has y-intercept.
$y = 3x$. Only $y = 3x$ passes through origin; $y = 3x + 2$ has y-intercept.
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What is the equation for earnings $E$ proportional to hours $h$ at hourly rate $r$?
What is the equation for earnings $E$ proportional to hours $h$ at hourly rate $r$?
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$E = rh$. Earnings equal hourly rate times hours worked.
$E = rh$. Earnings equal hourly rate times hours worked.
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Write the proportional equation if $y$ increases by $9$ when $x$ increases by $3$ and the relationship is proportional.
Write the proportional equation if $y$ increases by $9$ when $x$ increases by $3$ and the relationship is proportional.
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$y = 3x$. Rate of change is $\frac{9}{3} = 3$, so $y = 3x$.
$y = 3x$. Rate of change is $\frac{9}{3} = 3$, so $y = 3x$.
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What equation represents $y$ proportional to $x$ with constant of proportionality $k = \frac{3}{5}$?
What equation represents $y$ proportional to $x$ with constant of proportionality $k = \frac{3}{5}$?
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$y = \frac{3}{5}x$. Substitute $k = \frac{3}{5}$ into the general form $y = kx$.
$y = \frac{3}{5}x$. Substitute $k = \frac{3}{5}$ into the general form $y = kx$.
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Identify $k$ in the equation $y = 12x$.
Identify $k$ in the equation $y = 12x$.
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$k = 12$. The coefficient of $x$ is the constant of proportionality.
$k = 12$. The coefficient of $x$ is the constant of proportionality.
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Find $p$ if $t = 36$, $n = 8$, and $t = pn$.
Find $p$ if $t = 36$, $n = 8$, and $t = pn$.
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$p = \frac{9}{2}$. Solve $36 = p(8)$ by dividing both sides by $8$.
$p = \frac{9}{2}$. Solve $36 = p(8)$ by dividing both sides by $8$.
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What is the general equation for a proportional relationship between $y$ and $x$?
What is the general equation for a proportional relationship between $y$ and $x$?
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$y = kx$. Where $k$ is the constant ratio between $y$ and $x$.
$y = kx$. Where $k$ is the constant ratio between $y$ and $x$.
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What equation represents $y$ proportional to $x$ with constant of proportionality $k = 4$?
What equation represents $y$ proportional to $x$ with constant of proportionality $k = 4$?
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$y = 4x$. Substitute $k = 4$ into the general form $y = kx$.
$y = 4x$. Substitute $k = 4$ into the general form $y = kx$.
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What does the constant $k$ represent in the proportional equation $y = kx$?
What does the constant $k$ represent in the proportional equation $y = kx$?
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$k$ is the constant of proportionality (unit rate). It's the ratio $\frac{y}{x}$ that stays constant.
$k$ is the constant of proportionality (unit rate). It's the ratio $\frac{y}{x}$ that stays constant.
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Which equation represents “total cost $t$ equals price per item $p$ times number of items $n$”?
Which equation represents “total cost $t$ equals price per item $p$ times number of items $n$”?
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$t = pn$. Total equals rate times quantity in proportional relationships.
$t = pn$. Total equals rate times quantity in proportional relationships.
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Identify the constant of proportionality in the equation $t = pn$ (between $t$ and $n$).
Identify the constant of proportionality in the equation $t = pn$ (between $t$ and $n$).
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$p$. The coefficient of $n$ is the constant of proportionality.
$p$. The coefficient of $n$ is the constant of proportionality.
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What is the unit rate (constant of proportionality) if $ rac{y}{x} = 7$ for all $x \ne 0$?
What is the unit rate (constant of proportionality) if $ rac{y}{x} = 7$ for all $x \ne 0$?
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$k = 7$. Since $\frac{y}{x} = k$ in proportional relationships.
$k = 7$. Since $\frac{y}{x} = k$ in proportional relationships.
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Identify the constant of proportionality $k$ if the relationship is $y = -2x$.
Identify the constant of proportionality $k$ if the relationship is $y = -2x$.
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$k = -2$. The coefficient of $x$ in $y = -2x$ is $k = -2$.
$k = -2$. The coefficient of $x$ in $y = -2x$ is $k = -2$.
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What is $x$ when $y = \frac{3}{4}x$ and $y = 15$?
What is $x$ when $y = \frac{3}{4}x$ and $y = 15$?
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$x = 20$. Solve $15 = \frac{3}{4}x$: $x = 15 \times \frac{4}{3} = 20$.
$x = 20$. Solve $15 = \frac{3}{4}x$: $x = 15 \times \frac{4}{3} = 20$.
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What is the number of items $n$ if $t = 56$ dollars and $p = 8$ dollars per item?
What is the number of items $n$ if $t = 56$ dollars and $p = 8$ dollars per item?
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$n = 7$. Solve $56 = 8n$: $n = \frac{56}{8} = 7$.
$n = 7$. Solve $56 = 8n$: $n = \frac{56}{8} = 7$.
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Identify the equation if 3 tickets cost $24$ dollars and total cost $t$ is proportional to tickets $n$.
Identify the equation if 3 tickets cost $24$ dollars and total cost $t$ is proportional to tickets $n$.
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$t = 8n$. Find unit price: $\frac{24}{3} = 8$ dollars per ticket.
$t = 8n$. Find unit price: $\frac{24}{3} = 8$ dollars per ticket.
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What is the unit price $p$ if total cost is $t = 45$ dollars for $n = 9$ items?
What is the unit price $p$ if total cost is $t = 45$ dollars for $n = 9$ items?
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$p = 5$. Solve $45 = p(9)$: $p = \frac{45}{9} = 5$.
$p = 5$. Solve $45 = p(9)$: $p = \frac{45}{9} = 5$.
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