8th Grade Math Flashcards: Graph Proportional Relationships

What this deck covers

This deck focuses on Graph Proportional Relationships, giving you a quick way to review the definitions, rules, and examples that matter most for 8th 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: Compare speeds: Object A $d = 45t$ and Object B $d = 40t$. Which is faster?

Answer: Object A. Compare coefficients: $45 > 40$.

Flashcard 2: A car travels $180$ miles in $3$ hours. What is the speed (unit rate) in rac{ ext{miles}}{ ext{hour}}?

Answer: $60$. Speed = rac{ ext{distance}}{ ext{time}} = rac{180}{3}.

Flashcard 3: Choose the greater unit rate: $y = 2.5x$ or y = rac{11}{4}x.

Answer: y = rac{11}{4}x. rac{11}{4} = 2.75 > 2.5, so greater unit rate.

Flashcard 4: Identify the constant of proportionality for the table rule $y = 5x$.

Answer: $k = 5$. The coefficient of $x$ in $y = 5x$ is the constant.

Flashcard 5: Identify whether the relationship is proportional if the graph line crosses the $y$-axis at $2$.

Answer: Not proportional. Must pass through $(0,0)$ to be proportional.

Flashcard 6: What is the slope of the line y = -rac{3}{2}x?

Answer: -rac{3}{2}. The coefficient of $x$ is the slope.

Flashcard 7: What is the definition of a proportional relationship in terms of $y$ and $x$?

Answer: $y = kx$ for a constant $k$. Direct variation where $y$ is always $k$ times $x$.

Flashcard 8: Identify the slope of the line through $(0,0)$ and $(4,-10)$.

Answer: -rac{5}{2}. Use m = rac{-10-0}{4-0} = rac{-10}{4} = -rac{5}{2}

Flashcard 9: What is the slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$?

Answer: $m = \frac{y_2 - y_1}{x_2 - x_1}$. Rise over run gives the rate of change between points.

Flashcard 10: What point must be on the graph of any proportional relationship $y = kx$?

Answer: $(0,0)$. All proportional relationships pass through the origin.

Flashcard 11: Find $k$ for a proportional relationship where $y = 18$ when $x = 9$.

Answer: $k = 2$. Solve k = rac{y}{x} = rac{18}{9} = 2.

Flashcard 12: What is the unit rate in the equation $y = kx$?

Answer: $k$ (the value of $y$ when $x = 1$). The constant $k$ represents the rate of change per unit of $x$.

Flashcard 13: Which equation represents a proportional relationship: $y = 3x + 2$ or $y = 3x$?

Answer: $y = 3x$. Only $y = 3x$ passes through $(0,0)$.

Flashcard 14: What is the slope of the line representing $y = kx$ on a coordinate plane?

Answer: $k$. In $y = kx$, the coefficient $k$ is the slope.

Flashcard 15: Which object has greater speed: A passes through $(2,14)$ on a $d$ vs. $t$ graph, B has $d = 6t$?

Answer: Object A. A has slope rac{14}{2} = 7 > 6, so A is faster.

Flashcard 16: A proportional graph includes $(1,7)$. What is the equation in the form $y = kx$?

Answer: $y = 7x$. Since $(1,7)$ is on the line, k = rac{7}{1} = 7.

Flashcard 17: What is the slope of a distance-time graph if distance increases $150$ meters in $5$ seconds?

Answer: $30$. Slope = rac{Delta d}{Delta t} = rac{150}{5}.

Flashcard 18: What is the unit rate for the ratio rac{24}{6} (as $y$ per $x$)?

Answer: $4$. Divide $y$ by $x$: rac{24}{6} = 4.

Flashcard 19: Compare: A has slope $3$ on a $d$ vs. $t$ graph; B has equation $d = 2.8t$. Which is faster?

Answer: Object A. Slope $3 > 2.8$, so A is faster.

Flashcard 20: Find the slope of the proportional relationship through $(0,0)$ and $(3,12)$.

Answer: $m = 4$. Use $m = \frac{12-0}{3-0} = \frac{12}{3} = 4$.

Flashcard 21: What is the equation of a proportional relationship with unit rate $k=9$?

Answer: $y = 9x$. Substitute $k$ into the form $y = kx$.

Flashcard 22: Find the constant of proportionality $k$ if $y$ is proportional to $x$ and $(x,y)=(8,-20)$.

Answer: $k = \frac{-20}{8} = -\frac{5}{2}$. Use $k = \frac{y}{x}$ with the given point.

Flashcard 23: Which object is faster: A has slope $3$, B has slope $\frac{7}{2}$ (same units)?

Answer: B. Compare slopes: $\frac{7}{2} = 3.5 > 3$.

Flashcard 24: Which object is faster: A has $d=5t$, B has $d=4t$ (same units)?

Answer: A. Compare coefficients: $5 > 4$.

Flashcard 25: Choose the correct slope for a distance-time graph that goes through $(0,0)$ and $(4,30)$.

Answer: $\frac{30}{4} = 7.5$. Use slope formula: $\frac{30-0}{4-0}$.

Flashcard 26: What is the $y$-intercept of any proportional relationship graphed as a line on a coordinate plane?

Answer: $0$. All proportional relationships pass through $(0,0)$.

Flashcard 27: Find and correct the error: “For $y=\frac{3}{4}x$, the slope is $\frac{4}{3}$.” What is the correct slope?

Answer: Correct slope: $\frac{3}{4}$. The coefficient $\frac{3}{4}$ is the slope, not its reciprocal.

Flashcard 28: Which representation has the greater unit rate: $y=2.8x$ or a graph with slope $3.1$?

Answer: The graph with slope $3.1$. Compare unit rates: $3.1 > 2.8$.

Flashcard 29: Identify the slope for the proportional graph that passes through $(0,0)$ and $(2,-6)$.

Answer: $\frac{-6}{2} = -3$. Calculate slope using two points: $\frac{-6-0}{2-0}$.

Flashcard 30: What is the slope (unit rate) of a proportional relationship written as $y = kx$?

Answer: $k$. In $y = kx$, the coefficient $k$ represents the slope.