8th Grade Math Flashcards: Use Linear Models To Solve Problems

What this deck covers

This deck focuses on Use Linear Models To Solve Problems, 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: What are the units of intercept $b$ if $y$ is measured in dollars?

Answer: Dollars (same units as $y$). Intercept has the same units as the response variable.

Flashcard 2: What does the slope $m$ represent in a linear model $y = mx + b$ for bivariate measurement data?

Answer: Rate of change in $y$ for each $1$-unit increase in $x$. Slope measures how much $y$ changes per unit change in $x$.

Flashcard 3: What does the intercept $b$ represent in a linear model $y = mx + b$ for bivariate measurement data?

Answer: Predicted value of $y$ when $x = 0$. The $y$-intercept is where the line crosses the $y$-axis.

Flashcard 4: What is the slope $m$ of the line through $(2,5)$ and $(6,13)$?

Answer: $m = 2$. Use $m = \frac{13-5}{6-2} = \frac{8}{4} = 2$.

Flashcard 5: What is the intercept $b$ if $y = 3x + b$ passes through $(4,14)$?

Answer: $b = 2$. Substitute: $14 = 3(4) + b$, so $14 = 12 + b$.

Flashcard 6: What is the intercept $b$ if slope $m = 2$ and the line passes through $(0,9)$?

Answer: $b = 9$. When $x = 0$, $y = b$, so intercept equals $y$-coordinate.

Flashcard 7: Identify the slope and intercept in the model $y = -0.5x + 8$.

Answer: $m = -0.5$, $b = 8$. Coefficient of $x$ is slope; constant term is intercept.

Flashcard 8: What is the predicted change in $y$ when $x$ increases by $6$ in the model $y = 1.2x + 5$?

Answer: $\Delta y = 7.2$. Multiply slope by change in $x$: $1.2 \times 6 = 7.2$.

Flashcard 9: What is the linear model equation if slope $m = 4$ and intercept $b = -7$?

Answer: $y = 4x - 7$. Substitute slope and intercept into $y = mx + b$ form.

Flashcard 10: What is the predicted $y$ when $x = 5$ for the model $y = 2x + 3$?

Answer: $y = 13$. Substitute $x = 5$: $y = 2(5) + 3 = 10 + 3$.

Flashcard 11: What is the predicted $x$ when $y = 17$ for the model $y = 2x + 1$?

Answer: $x = 8$. Solve $17 = 2x + 1$: $16 = 2x$, so $x = 8$.

Flashcard 12: What does a slope of $1.5\ \text{cm/hr}$ mean in a model where $x$ is hours and $y$ is plant height?

Answer: Each additional $1$ hour predicts $1.5\ \text{cm}$ more height. Slope is the rate of change in context.

Flashcard 13: What does an intercept of $10\ \text{cm}$ mean in a model where $x$ is hours of sunlight and $y$ is height?

Answer: At $x = 0$, predicted height is $10\ \text{cm}$. Intercept is the starting value when input is zero.

Flashcard 14: Which variable is the explanatory variable in a model written as $y = mx + b$?

Answer: $x$ is the explanatory (independent) variable. In $y = mx + b$, $x$ is the input variable.

Flashcard 15: Which variable is the response variable in a model written as $y = mx + b$?

Answer: $y$ is the response (dependent) variable. In $y = mx + b$, $y$ depends on $x$.

Flashcard 16: What are the units of slope if $x$ is in hours and $y$ is in centimeters?

Answer: $\text{cm/hr}$. Slope units are output units per input unit.

Flashcard 17: What is the slope $m$ if $y$ increases by $12$ when $x$ increases by $3$?

Answer: $m = 4$. Slope equals change in $y$ divided by change in $x$: $\frac{12}{3}$.

Flashcard 18: What is the meaning of a negative slope in a bivariate linear model?

Answer: As $x$ increases, predicted $y$ decreases. Negative slope means inverse relationship.

Flashcard 19: What is the meaning of a slope of $0$ in a bivariate linear model?

Answer: Predicted $y$ stays constant as $x$ changes. Zero slope means a horizontal line.

Flashcard 20: What is the slope formula using two data 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 calculates slope between two points.

Flashcard 21: Find the slope of the line through $(2,7)$ and $(6,15)$.

Answer: $m = 2$. Use $m = \frac{15-7}{6-2} = \frac{8}{4}$.

Flashcard 22: Which value is the $y$-intercept in the model $y = 0.75x - 6$?

Answer: $-6$. Y-intercept is the constant term in $y = mx + b$.

Flashcard 23: Identify the meaning of $b$ in $y = 1.5x + 10$ if $x$ is hours of sunlight and $y$ is plant height (cm).

Answer: At $x = 0$, predicted height is $10$ cm. Y-intercept occurs when input is zero.

Flashcard 24: What does the phrase "predicted value" mean in a linear model context?

Answer: The model’s estimate of $y$ for a given $x$. Linear models predict output from input values.

Flashcard 25: What does a slope of $0$ mean about the relationship between $x$ and $y$ in a linear model?

Answer: Predicted $y$ does not change as $x$ changes. Zero slope means horizontal line.

Flashcard 26: What does a negative slope mean about the association between $x$ and $y$ in a linear model?

Answer: As $x$ increases, predicted $y$ decreases. Negative slope means inverse relationship.

Flashcard 27: What is the $y$-intercept in a linear model $y = mx + b$ and what does it represent in context?

Answer: $b$; the predicted value of $y$ when $x = 0$. Y-intercept is where the line crosses the y-axis.

Flashcard 28: What is the slope in a linear model $y = mx + b$ and what does it represent in context?

Answer: $m$; the change in $y$ for each $1$-unit increase in $x$. Slope measures rate of change between variables.

Flashcard 29: A model is $y = -1.2x + 50$. What is the predicted change in $y$ when $x$ increases by $5$?

Answer: Decrease of $6$. Change is slope times change in $x$: $-1.2 imes 5$.

Flashcard 30: A model is $y = 4x + 20$. What is the predicted change in $y$ when $x$ increases by $3$?

Answer: Increase of $12$. Change is slope times change in $x$: $4 imes 3$.