Graph Proportional Relationships - 8th Grade Math
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Compare speeds: Object A $d = 45t$ and Object B $d = 40t$. Which is faster?
Compare speeds: Object A $d = 45t$ and Object B $d = 40t$. Which is faster?
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Object A. Compare coefficients: $45 > 40$.
Object A. Compare coefficients: $45 > 40$.
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A car travels $180$ miles in $3$ hours. What is the speed (unit rate) in $ rac{ ext{miles}}{ ext{hour}}$?
A car travels $180$ miles in $3$ hours. What is the speed (unit rate) in $ rac{ ext{miles}}{ ext{hour}}$?
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$60$. Speed = $ rac{ ext{distance}}{ ext{time}} = rac{180}{3}$.
$60$. Speed = $ rac{ ext{distance}}{ ext{time}} = rac{180}{3}$.
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Choose the greater unit rate: $y = 2.5x$ or $y = rac{11}{4}x$.
Choose the greater unit rate: $y = 2.5x$ or $y = rac{11}{4}x$.
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$y = rac{11}{4}x$. $ rac{11}{4} = 2.75 > 2.5$, so greater unit rate.
$y = rac{11}{4}x$. $ rac{11}{4} = 2.75 > 2.5$, so greater unit rate.
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Identify the constant of proportionality for the table rule $y = 5x$.
Identify the constant of proportionality for the table rule $y = 5x$.
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$k = 5$. The coefficient of $x$ in $y = 5x$ is the constant.
$k = 5$. The coefficient of $x$ in $y = 5x$ is the constant.
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Identify whether the relationship is proportional if the graph line crosses the $y$-axis at $2$.
Identify whether the relationship is proportional if the graph line crosses the $y$-axis at $2$.
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Not proportional. Must pass through $(0,0)$ to be proportional.
Not proportional. Must pass through $(0,0)$ to be proportional.
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What is the slope of the line $y = - rac{3}{2}x$?
What is the slope of the line $y = - rac{3}{2}x$?
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$- rac{3}{2}$. The coefficient of $x$ is the slope.
$- rac{3}{2}$. The coefficient of $x$ is the slope.
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What is the definition of a proportional relationship in terms of $y$ and $x$?
What is the definition of a proportional relationship in terms of $y$ and $x$?
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$y = kx$ for a constant $k$. Direct variation where $y$ is always $k$ times $x$.
$y = kx$ for a constant $k$. Direct variation where $y$ is always $k$ times $x$.
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Identify the slope of the line through $(0,0)$ and $(4,-10)$.
Identify the slope of the line through $(0,0)$ and $(4,-10)$.
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$- rac{5}{2}$. Use $m = rac{-10-0}{4-0} = rac{-10}{4} = - rac{5}{2}$
$- rac{5}{2}$. Use $m = rac{-10-0}{4-0} = rac{-10}{4} = - rac{5}{2}$
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What is the slope formula between two points $ (x_1,y_1) $ and $ (x_2,y_2) $?
What is the slope formula between two points $ (x_1,y_1) $ and $ (x_2,y_2) $?
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$m = \frac{y_2 - y_1}{x_2 - x_1}$. Rise over run gives the rate of change between points.
$m = \frac{y_2 - y_1}{x_2 - x_1}$. Rise over run gives the rate of change between points.
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What point must be on the graph of any proportional relationship $y = kx$?
What point must be on the graph of any proportional relationship $y = kx$?
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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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Find $k$ for a proportional relationship where $y = 18$ when $x = 9$.
Find $k$ for a proportional relationship where $y = 18$ when $x = 9$.
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$k = 2$. Solve $k = rac{y}{x} = rac{18}{9} = 2$.
$k = 2$. Solve $k = rac{y}{x} = rac{18}{9} = 2$.
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What is the unit rate in the equation $y = kx$?
What is the unit rate in the equation $y = kx$?
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$k$ (the value of $y$ when $x = 1$). The constant $k$ represents the rate of change per unit of $x$.
$k$ (the value of $y$ when $x = 1$). The constant $k$ represents the rate of change per unit of $x$.
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Which equation represents a proportional relationship: $y = 3x + 2$ or $y = 3x$?
Which equation represents a proportional relationship: $y = 3x + 2$ or $y = 3x$?
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$y = 3x$. Only $y = 3x$ passes through $(0,0)$.
$y = 3x$. Only $y = 3x$ passes through $(0,0)$.
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What is the slope of the line representing $y = kx$ on a coordinate plane?
What is the slope of the line representing $y = kx$ on a coordinate plane?
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$k$. In $y = kx$, the coefficient $k$ is the slope.
$k$. In $y = kx$, the coefficient $k$ is the slope.
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Which object has greater speed: A passes through $(2,14)$ on a $d$ vs. $t$ graph, B has $d = 6t$?
Which object has greater speed: A passes through $(2,14)$ on a $d$ vs. $t$ graph, B has $d = 6t$?
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Object A. A has slope $ rac{14}{2} = 7 > 6$, so A is faster.
Object A. A has slope $ rac{14}{2} = 7 > 6$, so A is faster.
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A proportional graph includes $(1,7)$. What is the equation in the form $y = kx$?
A proportional graph includes $(1,7)$. What is the equation in the form $y = kx$?
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$y = 7x$. Since $(1,7)$ is on the line, $k = rac{7}{1} = 7$.
$y = 7x$. Since $(1,7)$ is on the line, $k = rac{7}{1} = 7$.
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What is the slope of a distance-time graph if distance increases $150$ meters in $5$ seconds?
What is the slope of a distance-time graph if distance increases $150$ meters in $5$ seconds?
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$30$. Slope = $ rac{Delta d}{Delta t} = rac{150}{5}$.
$30$. Slope = $ rac{Delta d}{Delta t} = rac{150}{5}$.
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What is the unit rate for the ratio $ rac{24}{6}$ (as $y$ per $x$)?
What is the unit rate for the ratio $ rac{24}{6}$ (as $y$ per $x$)?
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$4$. Divide $y$ by $x$: $ rac{24}{6} = 4$.
$4$. Divide $y$ by $x$: $ rac{24}{6} = 4$.
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Compare: A has slope $3$ on a $d$ vs. $t$ graph; B has equation $d = 2.8t$. Which is faster?
Compare: A has slope $3$ on a $d$ vs. $t$ graph; B has equation $d = 2.8t$. Which is faster?
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Object A. Slope $3 > 2.8$, so A is faster.
Object A. Slope $3 > 2.8$, so A is faster.
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Find the slope of the proportional relationship through $(0,0)$ and $(3,12)$.
Find the slope of the proportional relationship through $(0,0)$ and $(3,12)$.
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$m = 4$. Use $m = \frac{12-0}{3-0} = \frac{12}{3} = 4$.
$m = 4$. Use $m = \frac{12-0}{3-0} = \frac{12}{3} = 4$.
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What is the equation of a proportional relationship with unit rate $k=9$?
What is the equation of a proportional relationship with unit rate $k=9$?
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$y = 9x$. Substitute $k$ into the form $y = kx$.
$y = 9x$. Substitute $k$ into the form $y = kx$.
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Find the constant of proportionality $k$ if $y$ is proportional to $x$ and $(x,y)=(8,-20)$.
Find the constant of proportionality $k$ if $y$ is proportional to $x$ and $(x,y)=(8,-20)$.
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$k = \frac{-20}{8} = -\frac{5}{2}$. Use $k = \frac{y}{x}$ with the given point.
$k = \frac{-20}{8} = -\frac{5}{2}$. Use $k = \frac{y}{x}$ with the given point.
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Which object is faster: A has slope $3$, B has slope $\frac{7}{2}$ (same units)?
Which object is faster: A has slope $3$, B has slope $\frac{7}{2}$ (same units)?
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B. Compare slopes: $\frac{7}{2} = 3.5 > 3$.
B. Compare slopes: $\frac{7}{2} = 3.5 > 3$.
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Which object is faster: A has $d=5t$, B has $d=4t$ (same units)?
Which object is faster: A has $d=5t$, B has $d=4t$ (same units)?
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A. Compare coefficients: $5 > 4$.
A. Compare coefficients: $5 > 4$.
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Choose the correct slope for a distance-time graph that goes through $(0,0)$ and $(4,30)$.
Choose the correct slope for a distance-time graph that goes through $(0,0)$ and $(4,30)$.
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$\frac{30}{4} = 7.5$. Use slope formula: $\frac{30-0}{4-0}$.
$\frac{30}{4} = 7.5$. Use slope formula: $\frac{30-0}{4-0}$.
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What is the $y$-intercept of any proportional relationship graphed as a line on a coordinate plane?
What is the $y$-intercept of any proportional relationship graphed as a line on a coordinate plane?
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$0$. All proportional relationships pass through $(0,0)$.
$0$. All proportional relationships pass through $(0,0)$.
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Find and correct the error: “For $y=\frac{3}{4}x$, the slope is $\frac{4}{3}$.” What is the correct slope?
Find and correct the error: “For $y=\frac{3}{4}x$, the slope is $\frac{4}{3}$.” What is the correct slope?
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Correct slope: $\frac{3}{4}$. The coefficient $\frac{3}{4}$ is the slope, not its reciprocal.
Correct slope: $\frac{3}{4}$. The coefficient $\frac{3}{4}$ is the slope, not its reciprocal.
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Which representation has the greater unit rate: $y=2.8x$ or a graph with slope $3.1$?
Which representation has the greater unit rate: $y=2.8x$ or a graph with slope $3.1$?
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The graph with slope $3.1$. Compare unit rates: $3.1 > 2.8$.
The graph with slope $3.1$. Compare unit rates: $3.1 > 2.8$.
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Identify the slope for the proportional graph that passes through $(0,0)$ and $(2,-6)$.
Identify the slope for the proportional graph that passes through $(0,0)$ and $(2,-6)$.
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$\frac{-6}{2} = -3$. Calculate slope using two points: $\frac{-6-0}{2-0}$.
$\frac{-6}{2} = -3$. Calculate slope using two points: $\frac{-6-0}{2-0}$.
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What is the slope (unit rate) of a proportional relationship written as $y = kx$?
What is the slope (unit rate) of a proportional relationship written as $y = kx$?
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$k$. In $y = kx$, the coefficient $k$ represents the slope.
$k$. In $y = kx$, the coefficient $k$ represents the slope.
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