Analyze Dependent and Independent Variables - 6th Grade Math
Card 1 of 25
Identify the equation that matches the table $(x,y)$: $(0,1)$, $(1,3)$, $(2,5)$, $(3,7)$.
Identify the equation that matches the table $(x,y)$: $(0,1)$, $(1,3)$, $(2,5)$, $(3,7)$.
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$y = 2x + 1$. Pattern shows $y$ increases by $2$ for each unit increase in $x$.
$y = 2x + 1$. Pattern shows $y$ increases by $2$ for each unit increase in $x$.
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What is the dependent variable in an equation written as $y$ in terms of $x$?
What is the dependent variable in an equation written as $y$ in terms of $x$?
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$y$. The dependent variable's value depends on the independent variable.
$y$. The dependent variable's value depends on the independent variable.
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What is the independent variable in an equation written as $y$ in terms of $x$?
What is the independent variable in an equation written as $y$ in terms of $x$?
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$x$. The independent variable is chosen freely and determines the dependent variable.
$x$. The independent variable is chosen freely and determines the dependent variable.
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What does it mean to write one quantity “in terms of” another quantity?
What does it mean to write one quantity “in terms of” another quantity?
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Express one variable using the other variable. Write an equation showing how one variable is calculated from the other.
Express one variable using the other variable. Write an equation showing how one variable is calculated from the other.
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What ordered pair form matches “input, output” for independent and dependent variables?
What ordered pair form matches “input, output” for independent and dependent variables?
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$(x, y)$. Independent variable comes first, dependent variable second in ordered pairs.
$(x, y)$. Independent variable comes first, dependent variable second in ordered pairs.
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What is the equation for distance at constant speed $65$ mph after $t$ hours?
What is the equation for distance at constant speed $65$ mph after $t$ hours?
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$d = 65t$. Distance equals speed times time for constant motion.
$d = 65t$. Distance equals speed times time for constant motion.
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What is $d$ when $d = 65t$ and $t = 2$?
What is $d$ when $d = 65t$ and $t = 2$?
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$d = 130$. Substitute $t = 2$: $d = 65(2) = 130$.
$d = 130$. Substitute $t = 2$: $d = 65(2) = 130$.
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What is $t$ when $d = 65t$ and $d = 195$?
What is $t$ when $d = 65t$ and $d = 195$?
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$t = 3$. Solve $195 = 65t$ by dividing both sides by $65$.
$t = 3$. Solve $195 = 65t$ by dividing both sides by $65$.
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Which variable depends on time in the equation $d = 65t$: $d$ or $t$?
Which variable depends on time in the equation $d = 65t$: $d$ or $t$?
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$d$. Distance changes based on time, making it dependent.
$d$. Distance changes based on time, making it dependent.
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What is the constant of proportionality in the equation $d = 65t$?
What is the constant of proportionality in the equation $d = 65t$?
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$65$. The coefficient of $t$ represents the rate of change.
$65$. The coefficient of $t$ represents the rate of change.
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What is the y-intercept of the relationship $d = 65t$ in a $t$-$d$ graph?
What is the y-intercept of the relationship $d = 65t$ in a $t$-$d$ graph?
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$(0, 0)$. When $t = 0$, $d = 65(0) = 0$.
$(0, 0)$. When $t = 0$, $d = 65(0) = 0$.
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What is the slope of the line for $d = 65t$ when graphing $d$ versus $t$?
What is the slope of the line for $d = 65t$ when graphing $d$ versus $t$?
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$65$. Slope equals the coefficient of the independent variable.
$65$. Slope equals the coefficient of the independent variable.
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What is the correct ordered pair for $t = 4$ in the relationship $d = 65t$?
What is the correct ordered pair for $t = 4$ in the relationship $d = 65t$?
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$(4, 260)$. Substitute $t = 4$: $d = 65(4) = 260$.
$(4, 260)$. Substitute $t = 4$: $d = 65(4) = 260$.
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What is the equation for total cost with a $5$ dollar fee plus $2$ dollars per item $n$?
What is the equation for total cost with a $5$ dollar fee plus $2$ dollars per item $n$?
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$C = 2n + 5$. Fixed fee plus variable cost per item.
$C = 2n + 5$. Fixed fee plus variable cost per item.
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Which variable is independent in $C = 2n + 5$: $C$ or $n$?
Which variable is independent in $C = 2n + 5$: $C$ or $n$?
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$n$. Number of items is chosen; cost depends on it.
$n$. Number of items is chosen; cost depends on it.
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What is the equation for a starting height of $50$ cm that increases by $3$ cm per day $d$?
What is the equation for a starting height of $50$ cm that increases by $3$ cm per day $d$?
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$h = 50 + 3d$. Initial height plus growth rate times days.
$h = 50 + 3d$. Initial height plus growth rate times days.
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What is $h$ after $7$ days if $h = 50 + 3d$?
What is $h$ after $7$ days if $h = 50 + 3d$?
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$h = 71$. Substitute $d = 7$: $h = 50 + 3(7) = 71$.
$h = 71$. Substitute $d = 7$: $h = 50 + 3(7) = 71$.
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What is the independent variable in $h = 50 + 3d$?
What is the independent variable in $h = 50 + 3d$?
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$d$. Days are chosen; height depends on days.
$d$. Days are chosen; height depends on days.
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Which point is on the graph of $y = 2x + 1$: $(2,5)$ or $(2,6)$?
Which point is on the graph of $y = 2x + 1$: $(2,5)$ or $(2,6)$?
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$(2, 5)$. Check: $y = 2(2) + 1 = 5$ ✓.
$(2, 5)$. Check: $y = 2(2) + 1 = 5$ ✓.
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What is $C$ when $m = 4$ in the relationship $C = 2m + 5$?
What is $C$ when $m = 4$ in the relationship $C = 2m + 5$?
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$13$. Substitute: $C=2(4)+5=8+5=13$.
$13$. Substitute: $C=2(4)+5=8+5=13$.
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What does it mean for a variable to be independent in a relationship between two quantities?
What does it mean for a variable to be independent in a relationship between two quantities?
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It is the input you choose; the other variable depends on it. You control this value; it determines the other.
It is the input you choose; the other variable depends on it. You control this value; it determines the other.
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What is the equation for distance $d$ after $t$ hours at a constant speed of $65$ miles per hour?
What is the equation for distance $d$ after $t$ hours at a constant speed of $65$ miles per hour?
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$d = 65t$. Distance equals speed times time.
$d = 65t$. Distance equals speed times time.
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What ordered pair $(t,d)$ matches $d = 65t$ when $t = 2$?
What ordered pair $(t,d)$ matches $d = 65t$ when $t = 2$?
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$(2,130)$. Substitute $t=2$: $d=65(2)=130$.
$(2,130)$. Substitute $t=2$: $d=65(2)=130$.
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What does it mean for a variable to be dependent in a relationship between two quantities?
What does it mean for a variable to be dependent in a relationship between two quantities?
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It is the output that changes based on the other variable. Its value is determined by the independent variable.
It is the output that changes based on the other variable. Its value is determined by the independent variable.
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What is $C$ when $m = 6$ for the relationship $C = 5 + 2m$?
What is $C$ when $m = 6$ for the relationship $C = 5 + 2m$?
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$17$. Substitute: $C = 5 + 2(6) = 5 + 12 = 17$.
$17$. Substitute: $C = 5 + 2(6) = 5 + 12 = 17$.
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