8th Grade Math Flashcards: Fit Lines To Scatter Plots

What this deck covers

This deck focuses on Fit Lines To Scatter Plots, 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 is a positive linear association in a scatter plot?

Answer: As $x$ increases, $y$ tends to increase. Both variables move in the same direction together.

Flashcard 2: What is the residual if actual $y=7$ and predicted $y=10$?

Answer: Residual $=7-10=-3$. Actual minus predicted gives negative when point is below line.

Flashcard 3: What does it mean if points are widely scattered from a fitted line?

Answer: The linear model is a weak fit (weak linear association). Large scatter suggests the line poorly represents the data pattern.

Flashcard 4: What is a scatter plot used for when studying two quantitative variables?

Answer: A graph that plots $(x,y)$ pairs to show the relationship between two variables. Visualizes how two quantitative variables relate to each other.

Flashcard 5: What does a positive linear association look like in a scatter plot?

Answer: Points trend upward from left to right as $x$ increases. Shows a positive correlation between the variables.

Flashcard 6: Identify the slope sign if a fitted line goes down from left to right.

Answer: Negative slope, $m < 0$. Falling lines have negative slopes.

Flashcard 7: What is an outlier in a scatter plot?

Answer: A point far from the overall pattern of the data. Outliers can significantly affect the line of best fit.

Flashcard 8: What is a line of best fit used for in a scatter plot?

Answer: To model the relationship and make predictions. The line helps estimate values and understand trends.

Flashcard 9: What is one key rule for informally drawing a line of best fit?

Answer: Place about half the points above and half below the line. This balances the line through the data's center.

Flashcard 10: What does it mean when a scatter plot shows a linear association?

Answer: Points trend around a straight line as $x$ changes. Linear association means data follows a straight-line pattern.

Flashcard 11: What does it mean if a scatter plot shows no linear association?

Answer: There is no clear upward or downward linear trend. Points are scattered randomly without a linear pattern.

Flashcard 12: What is a negative linear association in a scatter plot?

Answer: As $x$ increases, $y$ tends to decrease. Variables move in opposite directions.

Flashcard 13: What is another key rule for informally drawing a line of best fit?

Answer: Draw the line through the middle of the point cluster. The line should represent the overall trend of all points.

Flashcard 14: What does a strong linear association look like in a scatter plot?

Answer: Points lie close to a straight line. Little scatter means the linear model fits well.

Flashcard 15: What does a weak linear association look like in a scatter plot?

Answer: Points are widely scattered around any line. Large scatter means the linear model fits poorly.

Flashcard 16: If a data point is at $(3,9)$ and the model predicts $y = 7$ at $x = 3$, what is the residual?

Answer: Residual $= 2$. Residual = actual - predicted = $9 - 7 = 2$.

Flashcard 17: If a fitted line is $y = -3x + 10$, what is the predicted $y$ when $x = 2$?

Answer: $y = 4$. Substitute: $y = -3(2) + 10 = -6 + 10 = 4$.

Flashcard 18: If a fitted line has equation $y = 2x + 1$, what is the predicted $y$ when $x = 4$?

Answer: $y = 9$. Substitute: $y = 2(4) + 1 = 8 + 1 = 9$.

Flashcard 19: Find the slope of the line through $(1,8)$ and $(5,2)$.

Answer: $m = -\frac{3}{2}$. $m = \frac{2-8}{5-1} = \frac{-6}{4} = -\frac{3}{2}$.

Flashcard 20: What does it mean to assess model fit informally on a scatter plot?

Answer: Judge how close the points are to the fitted line. Closer points mean better model accuracy.

Flashcard 21: Which model fit is better: points tightly clustered or widely scattered around a line?

Answer: Tightly clustered points indicate a better fit. Less scatter means more reliable predictions.

Flashcard 22: Identify the slope sign if a fitted line goes up from left to right.

Answer: Positive slope, $m > 0$. Rising lines have positive slopes.

Flashcard 23: Find the $y$ value on the line $y=3x+2$ when $x=4$.

Answer: $y=14$. Substitute $x=4$: $y=3(4)+2=12+2$.

Flashcard 24: Which option is usually less reliable for a fitted line: interpolation or extrapolation?

Answer: Extrapolation. Predictions beyond data range are less certain.

Flashcard 25: Identify the term for predicting $y$ for an $x$ value outside the data range using a fitted line.

Answer: Extrapolation. Making predictions beyond the observed data range.

Flashcard 26: What is the residual if the line predicts y=20 but the actual value is $y=16$?

Answer: $16-20=-4$. Residual = actual - predicted value.

Flashcard 27: Find the $y$ value on the line $y=-2x+10$ when $x=6$.

Answer: $y=-2$. Substitute $x=6$: $y=-2(6)+10=-12+10$.

Flashcard 28: What does a negative linear association look like in a scatter plot?

Answer: Points trend downward from left to right as $x$ increases. Shows a negative correlation between the variables.

Flashcard 29: What does it mean if points are widely scattered around a fitted line?

Answer: The linear model is a poor fit (weak linear association). Points deviate significantly from the line.

Flashcard 30: What is the slope between points $(1,9)$ and $(5,1)$?

Answer: rac{1-9}{5-1}=-2. Use slope formula: rac{y_2-y_1}{x_2-x_1}.