SAT Math Flashcards: Linear And Exponential Growth

What this deck covers

This deck focuses on Linear And Exponential Growth, giving you a quick way to review the definitions, rules, and examples that matter most for SAT 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: Find the slope in the equation $y = -5x + 3$.

Answer: -5. The coefficient of $x$ is the slope.

Flashcard 2: What is the formula for exponential growth?

Answer: $y = a(1 + r)^t$. Where $a$ is initial value, $r$ is growth rate, $t$ is time.

Flashcard 3: What is the initial value in the function $y = 7 \times 3^x$?

Answer:

1. The coefficient $a$ represents the starting value.

Flashcard 4: Find the slope of the line $y = \frac{1}{2}x + 2$.

Answer: $\frac{1}{2}$. The coefficient of $x$ gives the slope.

Flashcard 5: What is the value of $y$ when $x = 3$ in $y = 2x + 1$?

Answer:

1. Substitute $x = 3$: $y = 2(3) + 1 = 7$.

Flashcard 6: Identify the growth factor in $y = 7 \times 4^x$.

Answer:

1. The base $b$ determines the multiplication factor.

Flashcard 7: Identify the growth factor in the function $y = 7(1.5)^t$.

Answer: 1.5. The base of the exponential expression.

Flashcard 8: Which function represents linear growth?

Answer: $y = mx + b$. Constant rate of change defines linear functions.

Flashcard 9: Identify the slope in the equation $y = 3x + 5$.

Answer:

1. The coefficient of $x$ is the slope in slope-intercept form.

Flashcard 10: Identify the initial value in $y = 8 \times 2^x$.

Answer:

1. The coefficient $a$ is the starting value.

Flashcard 11: Which function represents exponential decay?

Answer: $y = a \times b^x$ with $0 < b < 1$. Base between 0 and 1 causes exponential decay.

Flashcard 12: Which function represents exponential decay?

Answer: $y = a \times b^x$ where $0 < b < 1$. When $0 < b < 1$, the function decreases as $x$ increases.

Flashcard 13: Determine if $y = -3 \times (0.5)^x$ is growth or decay.

Answer: Decay. Base $0.5 < 1$ indicates exponential decay.

Flashcard 14: Which function represents exponential growth?

Answer: $y = a \times b^x$ where $b > 1$. When $b > 1$, the function increases as $x$ increases.

Flashcard 15: What does the graph of $y = -2^x$ represent?

Answer: Reflect exponential decay. Negative coefficient reflects the exponential across x-axis.

Flashcard 16: What is the slope of a horizontal line?

Answer:

1. No vertical change means zero slope.

Flashcard 17: Which function shows exponential decay? $y = 2(0.8)^x$ or $y = 2(1.2)^x$?

Answer: $y = 2(0.8)^x$. Base $0.8 < 1$ indicates decay, while $1.2 > 1$ indicates growth.

Flashcard 18: Find the slope of the line through points $(1, 2)$ and $(3, 8)$.

Answer:

1. Using slope formula: $\frac{8-2}{3-1} = \frac{6}{2} = 3$.

Flashcard 19: Identify the growth rate if $y = a \times (1 + r)^x$ and $r = 0.08$.

Answer: 8%. Growth rate $r = 0.08 = 8\%$.

Flashcard 20: What is the slope of a horizontal line?

Answer:

1. No vertical change means zero slope.

Flashcard 21: What is the formula for exponential growth?

Answer: $y = a(1 + r)^t$. Where $a$ is initial value, $r$ is growth rate, $t$ is time.

Flashcard 22: What does $b$ represent in the linear equation $y = mx + b$?

Answer: Y-intercept. The value where the line crosses the y-axis.

Flashcard 23: Identify the slope in the equation $y = 3x + 7$.

Answer:

1. The coefficient of $x$ represents the slope.

Flashcard 24: Which function represents exponential growth?

Answer: $y = a \times b^x$ where $b > 1$. When $b > 1$, the function increases as $x$ increases.

Flashcard 25: What does $m$ represent in the linear equation $y = mx + b$?

Answer: Slope. Rate of change per unit increase in $x$.

Flashcard 26: State the y-intercept of $y = a \times b^x$ where $b > 0$.

Answer: $a$. Initial value when $x = 0$, since $b^0 = 1$.

Flashcard 27: Determine if $y = -3 \times (0.5)^x$ is growth or decay.

Answer: Decay. Base $0.5 < 1$ indicates exponential decay.

Flashcard 28: What is the general formula for a linear function?

Answer: $y = mx + b$. Standard slope-intercept form where $m$ is slope and $b$ is y-intercept.

Flashcard 29: What characteristic of a line does $b$ in $y = mx + b$ represent?

Answer: Y-intercept. Where the line crosses the y-axis at $(0, b)$.

Flashcard 30: What is the y-intercept in $y = 0.5 \times 3^x$?

Answer: 0.5. The initial value $a$ when $x = 0$.

Flashcard 31: Identify the exponential function with $a = 5$ and $b = 0.5$.

Answer: $y = 5 \times 0.5^x$. Exponential form with given initial value and base.

Flashcard 32: What does $b$ represent in the linear equation $y = mx + b$?

Answer: Y-intercept. The value where the line crosses the y-axis.

Flashcard 33: What is the slope of a vertical line?

Answer: Undefined. Division by zero in slope formula makes it undefined.

Flashcard 34: What is the general formula for an exponential function?

Answer: $y = a \times b^x$. Where $a$ is initial value and $b$ is the growth/decay factor.

Flashcard 35: What does $r$ represent in the exponential growth formula $y = a(1 + r)^t$?

Answer: Growth rate. The decimal or percentage increase per time unit.

Flashcard 36: Determine the y-intercept of $y = -3x + 6$.

Answer:

1. The constant term is the y-intercept.

Flashcard 37: What is the general formula for an exponential function?

Answer: $y = a \times b^x$. Where $a$ is initial value and $b$ is the growth/decay factor.

Flashcard 38: Identify the y-intercept in $y = -2x + 4$.

Answer:

1. The constant term gives the y-intercept.

Flashcard 39: Identify the growth factor in the function $y = 7(1.5)^t$.

Answer: 1.5. The base of the exponential expression.

Flashcard 40: Calculate $y$ when $x = 2$ for $y = 3 \times 2^x$.

Answer:

1. Substitute: $y = 3 \times 2^2 = 3 \times 4 = 12$.

Flashcard 41: What is the effect of $b = 1$ in $y = a \times b^x$?

Answer: Constant function. When $b = 1$, $b^x = 1$ for all $x$, so $y = a$.

Flashcard 42: What characteristic of a line does $b$ in $y = mx + b$ represent?

Answer: Y-intercept. Where the line crosses the y-axis at $(0, b)$.

Flashcard 43: Determine the y-intercept of the line $y = -2x + 4$.

Answer:

1. The constant term gives the y-intercept value.

Flashcard 44: Identify the growth factor in $y = 7 \times 4^x$.

Answer:

1. The base $b$ determines the multiplication factor.

Flashcard 45: Find the slope of the line $y = \frac{1}{2}x + 2$.

Answer: $\frac{1}{2}$. The coefficient of $x$ gives the slope.

Flashcard 46: Identify the growth type: $y = 5(1.08)^t$.

Answer: Exponential growth. Base 1.08 > 1 indicates growth with 8% rate.

Flashcard 47: Find the y-intercept of the line passing through $(0, -3)$.

Answer: -3. The y-coordinate when $x = 0$.

Flashcard 48: Determine the growth factor in $y = 2 \times 5^x$.

Answer:

1. The base $b$ determines how fast the function grows or decays.

Flashcard 49: Find the slope in the equation $y = -5x + 3$.

Answer: -5. The coefficient of $x$ is the slope.

Flashcard 50: Which function shows exponential decay? $y = 2(0.8)^x$ or $y = 2(1.2)^x$?

Answer: $y = 2(0.8)^x$. Base $0.8 < 1$ indicates decay, while $1.2 > 1$ indicates growth.

Flashcard 51: What does $r$ represent in $y = a \times (1 + r)^x$?

Answer: Growth rate. The percentage rate of growth per time period.

Flashcard 52: What is the slope of a vertical line?

Answer: Undefined. Division by zero in slope formula makes it undefined.

Flashcard 53: What does the graph of $y = -2^x$ represent?

Answer: Reflect exponential decay. Negative coefficient reflects the exponential across x-axis.

Flashcard 54: What is the formula for linear growth?

Answer: $y = mx + b$. Standard form where $m$ is slope and $b$ is y-intercept.

Flashcard 55: What is the y-intercept in $y = 0.5 \times 3^x$?

Answer: 0.5. The initial value $a$ when $x = 0$.

Flashcard 56: Identify the growth rate if $y = a \times (1 + r)^x$ and $r = 0.08$.

Answer: 8%. Growth rate $r = 0.08 = 8\%$.

Flashcard 57: What type of function does $y = 2(x - 3)^2 + 1$ represent?

Answer: Quadratic. Contains $x^2$ term making it a second-degree polynomial.

Flashcard 58: Find the y-intercept of the line passing through $(0, -3)$.

Answer: -3. The y-coordinate when $x = 0$.

Flashcard 59: Determine the slope of the line through $(1, 2)$ and $(3, 6)$.

Answer:

1. Using slope formula: $\frac{6-2}{3-1} = \frac{4}{2} = 2$.

Flashcard 60: What is the formula to find the slope 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 formula for calculating slope.

Flashcard 61: What is the effect of $b = 1$ in $y = a \times b^x$?

Answer: Constant function. When $b = 1$, $b^x = 1$ for all $x$, so $y = a$.

Flashcard 62: What is the formula for linear growth?

Answer: $y = mx + b$. Standard form where $m$ is slope and $b$ is y-intercept.

Flashcard 63: State the initial value in the exponential function $y = 5(1.2)^x$.

Answer:

1. The coefficient before the parentheses is the initial value.

Flashcard 64: Which function represents exponential decay?

Answer: $y = a \times b^x$ with $0 < b < 1$. Base between 0 and 1 causes exponential decay.

Flashcard 65: Calculate the slope of a line through $(2, 4)$ and $(6, 8)$.

Answer:

1. Using slope formula: $\frac{8-4}{6-2} = \frac{4}{4} = 1$.

Flashcard 66: Identify the y-intercept in $y = -2x + 4$.

Answer:

1. The constant term gives the y-intercept.

Flashcard 67: What is the formula for linear growth?

Answer: $y = mx + b$. Standard form where $m$ is slope and $b$ is y-intercept.

Flashcard 68: Identify the function type: $y = 5x^2 - 3x + 1$.

Answer: Quadratic. Highest power of $x$ is 2, making it quadratic.

Flashcard 69: Identify the y-intercept in the equation $y = 4x - 7$.

Answer: -7. The constant term is the y-intercept in slope-intercept form.

Flashcard 70: Determine the y-intercept of $y = -3x + 6$.

Answer:

1. The constant term is the y-intercept.

Flashcard 71: Determine the growth factor in $y = 2 \times 5^x$.

Answer: $5$. The base $b$ determines how fast the function grows or decays.

Flashcard 72: What type of function does $y = 2(x - 3)^2 + 1$ represent?

Answer: Quadratic. Contains $x^2$ term making it a second-degree polynomial.

Flashcard 73: Identify the slope in the equation $y = 3x + 5$.

Answer:

1. The coefficient of $x$ is the slope in slope-intercept form.

Flashcard 74: What is the formula to find the slope 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 formula for calculating slope.

Flashcard 75: What does the graph of $y = 2^x$ look like?

Answer: Exponential growth. Exponential function with base greater than 1 shows growth.

Flashcard 76: Which function represents exponential decay?

Answer: $y = a(1 - r)^t$. Uses $(1-r)$ where $0 < (1-r) < 1$ for decay.

Flashcard 77: State the y-intercept of $y = a \times b^x$ where $b > 0$.

Answer: $a$. Initial value when $x = 0$, since $b^0 = 1$.

Flashcard 78: Identify the initial value in $y = 8 \times 2^x$.

Answer:

1. The coefficient $a$ is the starting value.

Flashcard 79: Determine the equation if a line passes through $(2, 3)$ with slope $4$.

Answer: $y = 4x - 5$. Using point-slope form: $y - 3 = 4(x - 2)$.

Flashcard 80: Find $y$ when $x = 0$ in $y = 4 \times 10^x$.

Answer:

1. When $x = 0$: $y = 4 \times 10^0 = 4 \times 1 = 4$.

Flashcard 81: Identify the exponential function with $a = 5$ and $b = 0.5$.

Answer: $y = 5 \times 0.5^x$. Exponential form with given initial value and base.

Flashcard 82: What does the graph of $y = 2^x$ look like?

Answer: Exponential growth. Exponential function with base greater than 1 shows growth.

Flashcard 83: What does $m$ represent in the linear equation $y = mx + b$?

Answer: Slope. Rate of change per unit increase in $x$.

Flashcard 84: Calculate $y$ when $x = 2$ for $y = 3 \times 2^x$.

Answer:

1. Substitute: $y = 3 \times 2^2 = 3 \times 4 = 12$.

Flashcard 85: What is the general formula for a linear function?

Answer: $y = mx + b$. Standard slope-intercept form where $m$ is slope and $b$ is y-intercept.

Flashcard 86: Which function represents exponential decay?

Answer: $y = a \times b^x$ where $0 < b < 1$. When $0 < b < 1$, the function decreases as $x$ increases.

Flashcard 87: Calculate the slope of a line through $(2, 4)$ and $(6, 8)$.

Answer:

1. Using slope formula: $\frac{8-4}{6-2} = \frac{4}{4} = 1$.

Flashcard 88: Find $y$ when $x = 0$ in $y = 4 \times 10^x$.

Answer:

1. When $x = 0$: $y = 4 \times 10^0 = 4 \times 1 = 4$.

Flashcard 89: Identify the function type: $y = 5x^2 - 3x + 1$.

Answer: Quadratic. Highest power of $x$ is 2, making it quadratic.

Flashcard 90: Identify the growth type: $y = 3x + 2$.

Answer: Linear growth. Has constant slope of 3 and y-intercept of 2.

Flashcard 91: Find $y$ when $x = 1$ for $y = 3^x + 2$.

Answer:

1. Substitute $x = 1$: $y = 3^1 + 2 = 3 + 2 = 5$.

Flashcard 92: What is the initial value in the function $y = 7 \times 3^x$?

Answer:

1. The coefficient $a$ represents the starting value.

Flashcard 93: Identify the growth type: $y = 3x + 2$.

Answer: Linear growth. Has constant slope of 3 and y-intercept of 2.

Flashcard 94: What does $r$ represent in $y = a \times (1 + r)^x$?

Answer: Growth rate. The percentage rate of growth per time period.

Flashcard 95: What is the value of $y$ when $x = 3$ in $y = 2x + 1$?

Answer:

1. Substitute $x = 3$: $y = 2(3) + 1 = 7$.

Flashcard 96: Identify the y-intercept in the equation $y = 4x - 7$.

Answer: -7. The constant term is the y-intercept in slope-intercept form.

Flashcard 97: Find $y$ when $x = 1$ for $y = 3^x + 2$.

Answer:

1. Substitute $x = 1$: $y = 3^1 + 2 = 3 + 2 = 5$.

Flashcard 98: Determine the slope of the line through $(1, 2)$ and $(3, 6)$.

Answer:

1. Using slope formula: $\frac{6-2}{3-1} = \frac{4}{2} = 2$.

Flashcard 99: Which function represents linear growth?

Answer: $y = mx + b$. Constant rate of change defines linear functions.

Flashcard 100: Determine the y-intercept of the line $y = -2x + 4$.

Answer:

1. The constant term gives the y-intercept value.