Interpret Points on Proportional Graphs - 7th Grade Math
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A proportional relationship has unit rate $r=5$. What is the point on the graph when $x=1$?
A proportional relationship has unit rate $r=5$. What is the point on the graph when $x=1$?
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$(1,5)$. When $x=1$, $y$ equals the unit rate.
$(1,5)$. When $x=1$, $y$ equals the unit rate.
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Identify the point that shows the unit rate if $r=\frac{3}{4}$.
Identify the point that shows the unit rate if $r=\frac{3}{4}$.
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$(1,\frac{3}{4})$. When $x=1$, $y$ equals the unit rate $r$.
$(1,\frac{3}{4})$. When $x=1$, $y$ equals the unit rate $r$.
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Choose the correct interpretation of $(0,0)$ for $y=\frac{3}{2}x$: output is $0$ when input is $0$ or output is $\frac{3}{2}$ when input is $0$?
Choose the correct interpretation of $(0,0)$ for $y=\frac{3}{2}x$: output is $0$ when input is $0$ or output is $\frac{3}{2}$ when input is $0$?
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Output is $0$ when input is $0$. The origin represents zero of both quantities.
Output is $0$ when input is $0$. The origin represents zero of both quantities.
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Find the missing value $y$ if $y=3x$ and $x=7$.
Find the missing value $y$ if $y=3x$ and $x=7$.
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$y=21$. Multiply $x$ by the unit rate: $3 \times 7 = 21$.
$y=21$. Multiply $x$ by the unit rate: $3 \times 7 = 21$.
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Find the unit rate $r$ if a proportional graph contains the point $(4,10)$.
Find the unit rate $r$ if a proportional graph contains the point $(4,10)$.
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$r=\frac{10}{4}=\frac{5}{2}$. Divide $y$ by $x$ to find the constant rate.
$r=\frac{10}{4}=\frac{5}{2}$. Divide $y$ by $x$ to find the constant rate.
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A graph shows $5$ dollars for $2$ hours. What point represents this on a $(\text{hours},\text{dollars})$ graph?
A graph shows $5$ dollars for $2$ hours. What point represents this on a $(\text{hours},\text{dollars})$ graph?
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$(2,5)$. The ordered pair shows (input, output) values.
$(2,5)$. The ordered pair shows (input, output) values.
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What does the point $(0,0)$ mean in a proportional relationship context?
What does the point $(0,0)$ mean in a proportional relationship context?
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Zero input gives zero output. In proportional relationships, no input always produces no output.
Zero input gives zero output. In proportional relationships, no input always produces no output.
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Which point on a proportional graph directly shows the unit rate $r$: $(0,0)$ or $(1,r)$?
Which point on a proportional graph directly shows the unit rate $r$: $(0,0)$ or $(1,r)$?
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$(1,r)$. The $y$-coordinate equals $r$ when $x=1$.
$(1,r)$. The $y$-coordinate equals $r$ when $x=1$.
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What is the unit rate $r$ in the proportional relationship $y=rx$ in terms of $x$ and $y$?
What is the unit rate $r$ in the proportional relationship $y=rx$ in terms of $x$ and $y$?
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$r=\frac{y}{x}$ for $x\ne 0$. Divide output by input to find the constant ratio.
$r=\frac{y}{x}$ for $x\ne 0$. Divide output by input to find the constant ratio.
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What does the point $(1,r)$ mean on the graph of $y=rx$?
What does the point $(1,r)$ mean on the graph of $y=rx$?
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The output for $1$ unit of input is $r$ (unit rate). This special point reveals the constant of proportionality directly.
The output for $1$ unit of input is $r$ (unit rate). This special point reveals the constant of proportionality directly.
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What must be true about the graph of a proportional relationship in the coordinate plane?
What must be true about the graph of a proportional relationship in the coordinate plane?
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It is a straight line through $(0,0)$. Proportional relationships always pass through the origin.
It is a straight line through $(0,0)$. Proportional relationships always pass through the origin.
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What equation form describes any proportional relationship between $x$ and $y$ on a graph?
What equation form describes any proportional relationship between $x$ and $y$ on a graph?
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$y=rx$. The constant $r$ is the unit rate that relates $x$ and $y$ proportionally.
$y=rx$. The constant $r$ is the unit rate that relates $x$ and $y$ proportionally.
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What does the slope of a proportional relationship line represent in context?
What does the slope of a proportional relationship line represent in context?
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The unit rate $r$ (change in $y$ per $1$ in $x$). Slope equals the constant ratio between $y$ and $x$.
The unit rate $r$ (change in $y$ per $1$ in $x$). Slope equals the constant ratio between $y$ and $x$.
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Identify the $y$-intercept of any proportional relationship graph.
Identify the $y$-intercept of any proportional relationship graph.
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$(0,0)$. All proportional relationships pass through the origin.
$(0,0)$. All proportional relationships pass through the origin.
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Which statement is always true for a proportional relationship: $\frac{y}{x}$ is constant or $y-x$ is constant?
Which statement is always true for a proportional relationship: $\frac{y}{x}$ is constant or $y-x$ is constant?
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$\frac{y}{x}$ is constant. The ratio remains the same for all points on the line.
$\frac{y}{x}$ is constant. The ratio remains the same for all points on the line.
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What does a point $(x,y)$ represent on a graph of a proportional relationship in context?
What does a point $(x,y)$ represent on a graph of a proportional relationship in context?
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$x$ units of input correspond to $y$ units of output. Each coordinate shows the amount of one quantity for the given amount of the other.
$x$ units of input correspond to $y$ units of output. Each coordinate shows the amount of one quantity for the given amount of the other.
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Identify the constant of proportionality $r$ if the graph passes through $(6,2)$.
Identify the constant of proportionality $r$ if the graph passes through $(6,2)$.
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$r=\frac{2}{6}=\frac{1}{3}$
$r=\frac{2}{6}=\frac{1}{3}$
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What is the $y$-intercept of any proportional relationship graph $y=rx$?
What is the $y$-intercept of any proportional relationship graph $y=rx$?
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The $y$-intercept is $0$ (the graph passes through $(0,0)$)
The $y$-intercept is $0$ (the graph passes through $(0,0)$)
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Which point must be on every proportional relationship graph: $(0,0)$ or $(0,3)$?
Which point must be on every proportional relationship graph: $(0,0)$ or $(0,3)$?
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$(0,0)$
$(0,0)$
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What is the unit rate $r$ if a proportional graph contains the point $(1,5)$?
What is the unit rate $r$ if a proportional graph contains the point $(1,5)$?
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$r=5$
$r=5$
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Which graph feature shows a relationship is proportional: straight line through $(0,0)$ or any curve?
Which graph feature shows a relationship is proportional: straight line through $(0,0)$ or any curve?
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A straight line through $(0,0)$
A straight line through $(0,0)$
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Identify $y$ when $r=3$ and $x=7$ for a proportional relationship $y=rx$.
Identify $y$ when $r=3$ and $x=7$ for a proportional relationship $y=rx$.
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$y=21$
$y=21$
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Find $x$ when $r=\frac{1}{4}$ and $y=6$ for $y=rx$.
Find $x$ when $r=\frac{1}{4}$ and $y=6$ for $y=rx$.
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$x=24$
$x=24$
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What ratio is constant for every point $(x,y)$ on a proportional graph with $x\ne 0$?
What ratio is constant for every point $(x,y)$ on a proportional graph with $x\ne 0$?
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$\frac{y}{x}=r$
$\frac{y}{x}=r$
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A graph has points $(2,8)$ and $(5,20)$. Is it proportional based on $\frac{y}{x}$?
A graph has points $(2,8)$ and $(5,20)$. Is it proportional based on $\frac{y}{x}$?
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Yes, because $\frac{8}{2}=\frac{20}{5}=4$
Yes, because $\frac{8}{2}=\frac{20}{5}=4$
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