Algebra 2 Flashcards: Recognize Constant Rate Changes

What this deck covers

This deck focuses on Recognize Constant Rate Changes, giving you a quick way to review the definitions, rules, and examples that matter most for Algebra 2.

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 does a constant ratio $\frac{y}{x}$ (with $x\neq 0$) indicate about $y$ versus $x$?

Answer: A proportional linear relationship $y=kx$. Constant ratio means $y$ is proportional to $x$.

Flashcard 2: Identify whether this indicates constant rate: When $x$ increases by $2$, $y$ always increases by $10$.

Answer: Yes, constant rate ($m=5$). Fixed change of $10$ for every $2$ in $x$ means constant rate.

Flashcard 3: What is the constant rate if $y$ always increases by $10$ when $x$ increases by $2$?

Answer: $5$ per unit $x$. Rate per unit: $\frac{10}{2}=5$ per unit $x$.

Flashcard 4: What does it mean for $y$ to change at a constant rate per unit of $x$?

Answer: $\frac{\Delta y}{\Delta x}$ is constant for equal $\Delta x$ intervals. The ratio of change in $y$ to change in $x$ stays the same.

Flashcard 5: What must be true about slopes between any two pairs of points on a line?

Answer: They are equal (constant slope). All points on a line have the same slope between any pair.

Flashcard 6: What phrase most strongly signals constant rate: "per" or "percent"?

Answer: "Per" (constant additive rate per unit). "Per" indicates additive rate; "percent" indicates multiplicative rate.

Flashcard 7: What is the constant rate of change for the proportional relationship $y=5x$?

Answer: $5$. In $y=kx$, the constant $k$ is the rate.

Flashcard 8: Find the rate of change from $(-1,4)$ to $(3,-8)$.

Answer: $m=\frac{-8-4}{3-(-1)}=-3$. Using slope formula: $\frac{-8-4}{3-(-1)}=\frac{-12}{4}=-3$.

Flashcard 9: Identify whether the points $(0,1)$, $(1,2)$, $(2,4)$ show a constant rate of change.

Answer: No, slopes differ ($1$ then $2$). Slopes change from $1$ to $2$, so rate is not constant.

Flashcard 10: What is the constant rate of change in $y=2+4x$?

Answer: $4$. The coefficient of $x$ gives the rate of change.

Flashcard 11: Identify the constant rate in the verbal rule: "Start at $10$ and add $2$ each day."

Answer: $2$ per day. The additive change per time unit.

Flashcard 12: What is the constant rate of change for the line $3x-2y=8$?

Answer: $\frac{3}{2}$. Rearranging to $y=\frac{3}{2}x-4$ shows slope $\frac{3}{2}$.

Flashcard 13: Which change pattern indicates constant rate: constant differences in $y$ or constant ratios in $y$?

Answer: Constant differences in $y$ (for equal $\Delta x$). Constant differences indicate linear; constant ratios indicate exponential.

Flashcard 14: Identify whether the data show constant rate: $x:0,1,2$ and $y:5,8,11$.

Answer: Yes, constant rate ($\Delta y=3$ each step). Equal differences of $3$ between consecutive $y$-values.

Flashcard 15: Which equation form explicitly shows constant rate and initial value: $y=mx+b$ or $y=ax^2+c$?

Answer: $y=mx+b$. Linear form shows constant rate $m$ and starting value $b$.

Flashcard 16: Identify the constant rate of change for $y=-\frac{3}{2}x+8$.

Answer: $-\frac{3}{2}$. The coefficient of $x$ is the rate of change.

Flashcard 17: Identify whether this is constant rate: A tank loses $3$ liters every minute.

Answer: Yes, constant rate ($-3$ liters per minute). Fixed amount lost per time unit indicates constant rate.

Flashcard 18: Compute the unit rate if $\Delta y=-6$ when $\Delta x=3$.

Answer: $\frac{\Delta y}{\Delta x}=-2$. Divide change in $y$ by change in $x$: $\frac{-6}{3}=-2$.

Flashcard 19: Identify whether this indicates constant rate: When $x$ increases by $2$, $y$ always increases by $10$.

Answer: Yes, constant rate ($m=5$). Fixed change of $10$ for every $2$ in $x$ means constant rate.

Flashcard 20: Identify whether the sequence rule $y=2+4x$ represents constant change per step in $x$.

Answer: Yes, constant change of $4$ per $1$ in $x$. Linear form with coefficient $4$ as the constant rate.

Flashcard 21: Which description matches constant rate: "$y$ changes by a fixed amount" or "$y$ changes by a fixed factor"?

Answer: "$y$ changes by a fixed amount". Fixed amount indicates additive; fixed factor indicates multiplicative.

Flashcard 22: What does "constant percent rate" usually indicate: linear or exponential change?

Answer: Exponential change. Constant percent growth creates exponential patterns.

Flashcard 23: Identify the constant rate of change for $y=7x-3$.

Answer: $7$. The coefficient of $x$ is the rate of change.

Flashcard 24: Find the constant speed if distance is $60$ miles in $2$ hours at steady speed.

Answer: $30$ miles per hour. Rate equals distance divided by time: $\frac{60}{2}=30$.

Flashcard 25: Which relationship has constant rate: $y=x+3$ or $y=3^x$?

Answer: $y=x+3$. Linear has constant rate; exponential has constant ratio.

Flashcard 26: What table feature confirms a constant rate when $x$ increases by $1$ each row?

Answer: The first differences of $y$ are constant. Equal spacing in $x$ with constant $y$ differences confirms linearity.

Flashcard 27: Which statement indicates constant rate: "adds $4$ each hour" or "multiplies by $4$ each hour"?

Answer: "Adds $4$ each hour". Addition indicates constant rate, multiplication indicates exponential.

Flashcard 28: Identify whether the data show constant rate: $x:0,1,2$ and $y:5,9,16$.

Answer: No, first differences are not constant. Differences are $4$ then $7$, which are not equal.

Flashcard 29: Which situation represents constant rate: "$60$ miles in $2$ hours at steady speed" or "speeding up"?

Answer: "$60$ miles in $2$ hours at steady speed". Steady speed means constant rate; speeding up means changing rate.

Flashcard 30: What formula gives the constant rate of change between two points $(x_1,y_1)$ and $(x_2,y_2)$?

Answer: $m=\frac{y_2-y_1}{x_2-x_1}$. Standard slope formula using two points.