6th Grade Math Flashcards: Analyze Dependent And Independent Variables

What this deck covers

This deck focuses on Analyze Dependent And Independent Variables, giving you a quick way to review the definitions, rules, and examples that matter most for 6th Grade Math.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is the equation for total cost with a $5$ dollar fee plus $2$ dollars per item $n$?

Answer: $C = 2n + 5$. Fixed fee plus variable cost per item.

Flashcard 2: What is the independent variable in $d = 65t$, where $d$ is distance and $t$ is time?

Answer: $t$. Time is chosen first; distance depends on it.

Flashcard 3: Identify the equation that matches this table: $x: 0,1,2$ and $y: 3,5,7$.

Answer: $y = 2x + 3$. Each $x$ increase of $1$ gives $y$ increase of $2$, starting at $3$.

Flashcard 4: What is the equation for total cost $C$ with a $5$ dollar start fee plus $2$ dollars per mile $m$?

Answer: $C = 2m + 5$. Fixed fee plus variable cost per mile.

Flashcard 5: What is the independent variable in $d = 65t$ if $d$ is distance and $t$ is time?

Answer: $t$. Time is controlled/chosen; distance depends on it.

Flashcard 6: What does it mean for a variable to be dependent in a relationship between two quantities?

Answer: It is the output that changes based on the other variable. Its value is determined by the independent variable.

Flashcard 7: What is $t$ when $d = 260$ in the equation $d = 65t$?

Answer: $4$. Solve $260 = 65t$ by dividing both sides by $65$.

Flashcard 8: In $F = \frac{9}{5}C + 32$, which variable is independent if you choose the Celsius value first?

Answer: $C$. You input Celsius; Fahrenheit is calculated from it.

Flashcard 9: What is the dependent variable in $d = 65t$ if $d$ is distance and $t$ is time?

Answer: $d$. Distance depends on time; it changes based on how long you travel.

Flashcard 10: What is the constant of proportionality in the equation $d = 65t$?

Answer: $65$. The coefficient of $t$ represents the rate of change.

Flashcard 11: Which equation matches: "A taxi charges a $5$ dollar start fee plus $2$ dollars per mile $m$"?

Answer: $C = 5 + 2m$. Fixed fee plus variable rate per mile gives total cost.

Flashcard 12: Which equation expresses $y$ as a function of $x$ for a constant rate of $3$ and start value $-2$?

Answer: $y = 3x - 2$. Linear equation with slope $3$ and y-intercept $-2$.

Flashcard 13: What does the slope mean in $d = 65t$ when $d$ is miles and $t$ is hours?

Answer: $65$ miles per hour. The coefficient shows the constant speed.

Flashcard 14: What is the slope of the line for $d = 65t$ when graphing $d$ versus $t$?

Answer: $65$. Slope equals the coefficient of the independent variable.

Flashcard 15: What is the equation for distance $d$ after $t$ hours at a constant speed of $65$ miles per hour?

Answer: $d = 65t$. Distance equals speed times time.

Flashcard 16: What is the dependent variable in $d = 65t$, where $d$ is distance and $t$ is time?

Answer: $d$. Distance depends on the time traveled.

Flashcard 17: What is the y-intercept of the relationship $d = 65t$ in a $t$-$d$ graph?

Answer: $(0, 0)$. When $t = 0$, $d = 65(0) = 0$.

Flashcard 18: What is the $d$-intercept of $d = 65t$ (the value of $d$ when $t = 0$)?

Answer: $0$. When $t=0$, $d=65(0)=0$.

Flashcard 19: What ordered pair $(t,d)$ matches $d = 65t$ when $t = 2$?

Answer: $(2,130)$. Substitute $t=2$: $d=65(2)=130$.

Flashcard 20: What is $d$ when $t = 3$ in the equation $d = 65t$?

Answer: $195$. Substitute $t = 3$: $d = 65(3) = 195$.

Flashcard 21: What is the slope (rate of change) in $C = 5 + 2m$ when graphed as $(m, C)$?

Answer: $2$. Cost increases by $2 for each additional mile.

Flashcard 22: What is the equation for a starting height of $50$ cm that increases by $3$ cm per day $d$?

Answer: $h = 50 + 3d$. Initial height plus growth rate times days.

Flashcard 23: What does the negative slope mean in $M = 20 - 3d$ (money left vs. days)?

Answer: $M$ decreases by $3$ each time $d$ increases by $1$. Negative slope shows money decreases over time.

Flashcard 24: Which point is on the graph of $y = 2x + 1$: $(2,5)$ or $(2,6)$?

Answer: $(2, 5)$. Check: $y = 2(2) + 1 = 5$ ✓.

Flashcard 25: What is the y-intercept in $C = 5 + 2m$ when graphed as $(m, C)$?

Answer: $5$. When $m = 0$, $C = 5 + 2(0) = 5$ (initial fee).

Flashcard 26: What does the coefficient $65$ represent in $d = 65t$ (distance vs. time at constant speed)?

Answer: Speed is $65$ distance-units per $1$ time-unit. The constant rate shows distance covered per unit time.

Flashcard 27: Identify the correct table rule: if $(t, d)$ follows $d = 4t$, what is $d$ when $t = 7$?

Answer: $28$. Multiply: $d = 4(7) = 28$.

Flashcard 28: What is the dependent variable in an equation written as $y$ in terms of $x$?

Answer: $y$. The dependent variable's value depends on the independent variable.

Flashcard 29: What is $d$ when $d = 65t$ and $t = 2$?

Answer: $d = 130$. Substitute $t = 2$: $d = 65(2) = 130$.

Flashcard 30: What is $M$ when $d = 4$ for the equation $M = 20 - 3d$?

Answer: $8$. Substitute: $M = 20 - 3(4) = 20 - 12 = 8$.

Flashcard 31: What is the rate of change between consecutive points in the table $x: 0,1,2$ and $y: 3,5,7$?

Answer: $2$. Change in $y$ divided by change in $x$: rac{5-3}{1-0}=2.

Flashcard 32: Identify the equation for: "You have $20$ dollars and spend $3$ dollars per day $d$".

Answer: $M = 20 - 3d$. Start amount minus spending rate times days.

Flashcard 33: What is the meaning of the y-intercept in $y = 3x - 2$ when $x$ is the independent variable?

Answer: When $x = 0$, $y = -2$. Y-intercept is the value of $y$ when input $x$ equals zero.

Flashcard 34: In $C = 2m + 5$, which variable is dependent if $m$ is miles and $C$ is total cost?

Answer: $C$. Cost depends on miles traveled.

Flashcard 35: What is $h$ after $7$ days if $h = 50 + 3d$?

Answer: $h = 71$. Substitute $d = 7$: $h = 50 + 3(7) = 71$.

Flashcard 36: Which variable is dependent in $C = 5 + 2m$ if $m$ is miles and $C$ is total cost?

Answer: $C$. Cost depends on miles driven; it's the output variable.

Flashcard 37: What is $C$ when $m = 4$ in the relationship $C = 2m + 5$?

Answer: $13$. Substitute: $C=2(4)+5=8+5=13$.

Flashcard 38: What is $t$ when $d = 65t$ and $d = 195$?

Answer: $t = 3$. Solve $195 = 65t$ by dividing both sides by $65$.

Flashcard 39: What is the correct ordered pair for $t = 4$ in the relationship $d = 65t$?

Answer: $(4, 260)$. Substitute $t = 4$: $d = 65(4) = 260$.

Flashcard 40: Identify the equation that matches the table $(x,y)$: $(0,1)$, $(1,3)$, $(2,5)$, $(3,7)$.

Answer: $y = 2x + 1$. Pattern shows $y$ increases by $2$ for each unit increase in $x$.

Flashcard 41: Which variable is independent in $C = 2n + 5$: $C$ or $n$?

Answer: $n$. Number of items is chosen; cost depends on it.

Flashcard 42: What is the independent variable in $h = 50 + 3d$?

Answer: $d$. Days are chosen; height depends on days.

Flashcard 43: What is $F$ when $C = 0$ in $F = \frac{9}{5}C + 32$?

Answer: $32$. Water freezes at $0°C$ and $32°F$.

Flashcard 44: Which equation represents a line with slope $4$ and $y$-intercept $-1$?

Answer: $y = 4x - 1$. Slope-intercept form: $y=mx+b$ where $m=4$, $b=-1$.

Flashcard 45: What is the slope (rate of change) of the relationship $d = 65t$?

Answer: $65$. Coefficient of $t$ represents miles per hour.

Flashcard 46: What is $C$ when $m = 6$ for the relationship $C = 5 + 2m$?

Answer: $17$. Substitute: $C = 5 + 2(6) = 5 + 12 = 17$.

Flashcard 47: What is the independent variable in an equation written as $y$ in terms of $x$?

Answer: $x$. The independent variable is chosen freely and determines the dependent variable.

Flashcard 48: What does it mean for a variable to be independent in a relationship between two quantities?

Answer: It is the input you choose; the other variable depends on it. You control this value; it determines the other.

Flashcard 49: What ordered pair form matches "input, output" for independent and dependent variables?

Answer: $(x, y)$. Independent variable comes first, dependent variable second in ordered pairs.

Flashcard 50: What is $C$ when $C = 2n + 5$ and $n = 6$?

Answer: $C = 17$. Substitute $n = 6$: $C = 2(6) + 5 = 17$.

Flashcard 51: What does it mean to write one quantity "in terms of" another quantity?

Answer: Express one variable using the other variable. Write an equation showing how one variable is calculated from the other.

Flashcard 52: What is the equation for distance at constant speed $65$ mph after $t$ hours?

Answer: $d = 65t$. Distance equals speed times time for constant motion.

Flashcard 53: What is the height $h$ after $5$ weeks in $h = 10 + 2w$?

Answer: $20$. Substitute: $h = 10 + 2(5) = 10 + 10 = 20$.

Flashcard 54: What is the value of $d$ when $M = 0$ in $M = 20 - 3d$?

Answer: $\frac{20}{3}$. Solve $0 = 20 - 3d$: $3d = 20$, so $d = \frac{20}{3}$.

Flashcard 55: Identify the ordered pair format when graphing distance $d$ versus time $t$.

Answer: Plot $(t, d)$. Independent variable first, dependent second in ordered pairs.

Flashcard 56: Which equation matches: "A plant is $10$ cm tall and grows $2$ cm per week $w$"?

Answer: $h = 10 + 2w$. Initial height plus growth rate times weeks.

Flashcard 57: Which ordered pair $(t,d)$ is on the graph of $d = 65t$: $(3,195)$ or $(3,190)$?

Answer: $(3,195)$. Check: $65(3)=195$, not $190$.

Flashcard 58: Which variable depends on time in the equation $d = 65t$: $d$ or $t$?

Answer: $d$. Distance changes based on time, making it dependent.

Flashcard 59: What ordered pair $(m,C)$ matches $C = 2m + 5$ when $m = 0$?

Answer: $(0,5)$. At $0$ miles, only the $5$ start fee applies.