Identify Proportional Relationships - 7th Grade Math
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A graph is a straight line but crosses the $y$-axis at $(0,3)$. Is it proportional?
A graph is a straight line but crosses the $y$-axis at $(0,3)$. Is it proportional?
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No, not proportional. Must pass through $(0,0)$ to be proportional.
No, not proportional. Must pass through $(0,0)$ to be proportional.
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Identify whether the table is proportional: $x=0,2,4$ and $y=0,6,12$.
Identify whether the table is proportional: $x=0,2,4$ and $y=0,6,12$.
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Yes, proportional. Constant ratio $\frac{6}{2}=\frac{12}{4}=3$ and includes $(0,0)$.
Yes, proportional. Constant ratio $\frac{6}{2}=\frac{12}{4}=3$ and includes $(0,0)$.
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What ratio must stay equal in a proportional relationship between $x$ and $y$?
What ratio must stay equal in a proportional relationship between $x$ and $y$?
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$\frac{y}{x}$ is constant for $x\neq 0$. In proportional relationships, all ratios of $y$ to $x$ are equal.
$\frac{y}{x}$ is constant for $x\neq 0$. In proportional relationships, all ratios of $y$ to $x$ are equal.
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Identify whether the points form a proportional relationship: $(1,2)$, $(2,4)$, $(3,7)$.
Identify whether the points form a proportional relationship: $(1,2)$, $(2,4)$, $(3,7)$.
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No, not proportional. Ratio changes: $\frac{2}{1}=2$, $\frac{4}{2}=2$, but $\frac{7}{3}\approx 2.33$.
No, not proportional. Ratio changes: $\frac{2}{1}=2$, $\frac{4}{2}=2$, but $\frac{7}{3}\approx 2.33$.
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Identify whether the points form a proportional relationship: $(0,0)$, $(2,5)$, $(4,10)$.
Identify whether the points form a proportional relationship: $(0,0)$, $(2,5)$, $(4,10)$.
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Yes, proportional. All have constant ratio $\frac{5}{2}$ and include $(0,0)$.
Yes, proportional. All have constant ratio $\frac{5}{2}$ and include $(0,0)$.
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Find $x$ if $y$ is proportional to $x$ with $k=5$ and $y=35$.
Find $x$ if $y$ is proportional to $x$ with $k=5$ and $y=35$.
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$x=7$. Solve $35=5x$ to get $x=7$.
$x=7$. Solve $35=5x$ to get $x=7$.
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Find $y$ if $y$ is proportional to $x$ with $k=\frac{3}{4}$ and $x=8$.
Find $y$ if $y$ is proportional to $x$ with $k=\frac{3}{4}$ and $x=8$.
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$y=6$. Substitute: $y=\frac{3}{4}(8)=6$.
$y=6$. Substitute: $y=\frac{3}{4}(8)=6$.
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Identify whether the relationship is proportional: $y=\frac{4}{5}x-1$.
Identify whether the relationship is proportional: $y=\frac{4}{5}x-1$.
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No, not proportional. The $-1$ makes it not pass through $(0,0)$.
No, not proportional. The $-1$ makes it not pass through $(0,0)$.
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Identify whether the relationship is proportional: $y=\frac{4}{5}x$.
Identify whether the relationship is proportional: $y=\frac{4}{5}x$.
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Yes, proportional. Form $y=kx$ with $k=\frac{4}{5}$ passes through origin.
Yes, proportional. Form $y=kx$ with $k=\frac{4}{5}$ passes through origin.
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Choose the equation that represents a proportional relationship: $y=3x$ or $y=3x+2$.
Choose the equation that represents a proportional relationship: $y=3x$ or $y=3x+2$.
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$y=3x$. Only $y=3x$ passes through $(0,0)$; $y=3x+2$ has $y$-intercept $2$.
$y=3x$. Only $y=3x$ passes through $(0,0)$; $y=3x+2$ has $y$-intercept $2$.
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Identify whether $(3,8)$ and $(9,20)$ could be in the same proportional relationship.
Identify whether $(3,8)$ and $(9,20)$ could be in the same proportional relationship.
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No, not proportional. Different ratios: $\frac{8}{3}\approx 2.67$ vs $\frac{20}{9}\approx 2.22$.
No, not proportional. Different ratios: $\frac{8}{3}\approx 2.67$ vs $\frac{20}{9}\approx 2.22$.
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Identify whether $(2,7)$ and $(6,21)$ could be in the same proportional relationship.
Identify whether $(2,7)$ and $(6,21)$ could be in the same proportional relationship.
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Yes, proportional. Both have ratio $\frac{7}{2}=\frac{21}{6}=3.5$.
Yes, proportional. Both have ratio $\frac{7}{2}=\frac{21}{6}=3.5$.
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What is $k$ for a proportional relationship passing through $(6,4)$ and $(0,0)$?
What is $k$ for a proportional relationship passing through $(6,4)$ and $(0,0)$?
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$k=\frac{2}{3}$. Use $k=\frac{y}{x}=\frac{4}{6}=\frac{2}{3}$.
$k=\frac{2}{3}$. Use $k=\frac{y}{x}=\frac{4}{6}=\frac{2}{3}$.
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What is $k$ for a proportional relationship passing through $(4,10)$ and $(0,0)$?
What is $k$ for a proportional relationship passing through $(4,10)$ and $(0,0)$?
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$k=\frac{5}{2}$. Use $k=\frac{y}{x}=\frac{10}{4}=\frac{5}{2}$.
$k=\frac{5}{2}$. Use $k=\frac{y}{x}=\frac{10}{4}=\frac{5}{2}$.
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Identify whether the table is proportional: $(1,2)$, $(2,5)$, $(3,6)$.
Identify whether the table is proportional: $(1,2)$, $(2,5)$, $(3,6)$.
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No, not proportional. Ratios vary: $\frac{2}{1}=2$, $\frac{5}{2}=2.5$, $\frac{6}{3}=2$.
No, not proportional. Ratios vary: $\frac{2}{1}=2$, $\frac{5}{2}=2.5$, $\frac{6}{3}=2$.
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Identify whether the table is proportional: $(1,3)$, $(2,6)$, $(3,9)$.
Identify whether the table is proportional: $(1,3)$, $(2,6)$, $(3,9)$.
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Yes, proportional. All ratios equal $3$: $\frac{3}{1}=\frac{6}{2}=\frac{9}{3}=3$.
Yes, proportional. All ratios equal $3$: $\frac{3}{1}=\frac{6}{2}=\frac{9}{3}=3$.
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Which point must be on the graph of any proportional relationship?
Which point must be on the graph of any proportional relationship?
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$(0,0)$. The origin because when $x=0$, $y=0$ in $y=kx$.
$(0,0)$. The origin because when $x=0$, $y=0$ in $y=kx$.
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What must the graph of a proportional relationship look like on a coordinate plane?
What must the graph of a proportional relationship look like on a coordinate plane?
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A straight line through $(0,0)$. Proportional relationships always pass through the origin.
A straight line through $(0,0)$. Proportional relationships always pass through the origin.
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What is the constant of proportionality in the equation $y=kx$?
What is the constant of proportionality in the equation $y=kx$?
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$k$. The constant that relates $y$ to $x$ in direct proportion.
$k$. The constant that relates $y$ to $x$ in direct proportion.
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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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$y=kx$ for a constant $k$. Proportional means one quantity is a constant multiple of the other.
$y=kx$ for a constant $k$. Proportional means one quantity is a constant multiple of the other.
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Identify whether $(0,5)$ can be on a proportional graph of $y$ vs. $x$.
Identify whether $(0,5)$ can be on a proportional graph of $y$ vs. $x$.
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No; proportional graphs must include $(0,0)$
No; proportional graphs must include $(0,0)$
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Identify whether the points $(1,3)$ and $(2,6)$ are proportional to the origin.
Identify whether the points $(1,3)$ and $(2,6)$ are proportional to the origin.
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Yes; $\frac{3}{1} = \frac{6}{2} = 3$
Yes; $\frac{3}{1} = \frac{6}{2} = 3$
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Identify whether the points $(2,5)$ and $(4,10)$ show a proportional relationship.
Identify whether the points $(2,5)$ and $(4,10)$ show a proportional relationship.
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Yes; $\frac{5}{2} = \frac{10}{4}$
Yes; $\frac{5}{2} = \frac{10}{4}$
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Find $k$ for a proportional relationship passing through $(6,15)$.
Find $k$ for a proportional relationship passing through $(6,15)$.
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$k = \frac{15}{6} = \frac{5}{2}$
$k = \frac{15}{6} = \frac{5}{2}$
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Find $k$ for a proportional relationship passing through $(8,2)$.
Find $k$ for a proportional relationship passing through $(8,2)$.
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$k = \frac{2}{8} = \frac{1}{4}$
$k = \frac{2}{8} = \frac{1}{4}$
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