ISEE Middle Level Mathematics Achievement Flashcards: Table And Graph Interpretation

What this deck covers

This deck focuses on Table And Graph Interpretation, giving you a quick way to review the definitions, rules, and examples that matter most for ISEE Middle Level Mathematics Achievement.

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 horizontal line ($m=0$) mean about the relationship between $x$ and $y$?

Answer: $y$ is constant for all $x$ values. A zero slope signifies that the dependent variable remains unchanged regardless of variations in the independent variable.

Flashcard 2: What does the $x$-intercept represent on a graph of $y$ versus $x$?

Answer: The value of $x$ when $y=0$. The x-intercept is the point where the graph crosses the x-axis, indicating the input value that yields zero output.

Flashcard 3: What does a negative slope on a line graph indicate about $y$ as $x$ increases?

Answer: $y$ decreases as $x$ increases. A negative slope indicates an inverse relationship where the dependent variable falls as the independent variable rises.

Flashcard 4: Find the slope between $(2,5)$ and $(6,13)$.

Answer: $m=2$. Applying the slope formula gives a rise of 8 over a run of 4, resulting in the calculated value.

Flashcard 5: A table shows $(x,y)$ pairs: $(0,7)$, $(1,5)$, $(2,3)$. What is the change in $y$ per $+1$ in $x$?

Answer: $-2$ per $1$ unit of $x$. Each unit increase in x results in a consistent decrease of 2 in y, indicating a constant rate.

Flashcard 6: Identify the dependent variable on a standard graph where $x$ is time and $y$ is distance.

Answer: Distance (the $y$-variable). The dependent variable, often distance on the y-axis, varies based on changes in the independent variable.

Flashcard 7: What is the average rate of change of $y$ from $x=a$ to $x=b$ on a graph?

Answer: $\frac{y(b)-y(a)}{b-a}$. The average rate of change measures the overall slope of the secant line connecting the points at x=a and x=b.

Flashcard 8: A pie chart shows $\frac{1}{4}$ of students walk to school. What percent is this?

Answer: $25\%$. Converting the fraction 1/4 to a percentage by multiplying by 100 yields the result.

Flashcard 9: What does the $y$-intercept represent on a graph of $y$ versus $x$?

Answer: The value of $y$ when $x=0$. The y-intercept is the point where the graph intersects the y-axis, showing the output when the input is zero.

Flashcard 10: What is the slope between points $(x_1,y_1)$ and $(x_2,y_2)$?

Answer: $m=\frac{y_2-y_1}{x_2-x_1}$. The slope formula computes the rate of change as the difference in y-values divided by the difference in x-values between two points.

Flashcard 11: What is the $x$-intercept of the line $y=2x-10$?

Answer: $x=5$. Setting y=0 in the equation and solving for x determines the x-intercept.

Flashcard 12: What does the maximum value on a graph represent in the context of the data?

Answer: The greatest observed $y$-value (output). The maximum y-value identifies the peak output observed in the dataset represented by the graph.

Flashcard 13: What does the range of a graph's $y$-values mean for the data shown?

Answer: All output values $y$ that occur on the graph. The range encompasses all possible output values produced by the function over the graphed interval.

Flashcard 14: A bar chart has counts $A=12$, $B=9$, $C=15$. Which category has the greatest value?

Answer: $C$. Comparing the bar heights shows C with the tallest bar, indicating the highest count.

Flashcard 15: What do the coordinates $(x,y)$ of a point on a graph represent?

Answer: $x$ is the input (horizontal); $y$ is the output (vertical). In coordinate geometry, the x-coordinate denotes the independent variable on the horizontal axis, while y denotes the dependent variable on the vertical axis.

Flashcard 16: What does the minimum value on a graph represent in the context of the data?

Answer: The smallest observed $y$-value (output). The minimum y-value marks the lowest output point in the data depicted on the graph.

Flashcard 17: A bar chart has values $A=18$, $B=6$, $C=12$. What is the difference between the greatest and least values?

Answer: $12$. Subtracting the smallest value (6) from the largest (18) gives the range of the data.

Flashcard 18: What does a positive slope on a line graph indicate about $y$ as $x$ increases?

Answer: $y$ increases as $x$ increases. A positive slope reflects a direct relationship where the dependent variable rises with increases in the independent variable.

Flashcard 19: What is the $y$-intercept of the line through $(0,-3)$ and $(4,5)$?

Answer: $-3$. The point (0, -3) directly provides the y-intercept as it lies on the y-axis.

Flashcard 20: A line graph passes through $(2,8)$ and $(6,20)$. What is the average rate of change?

Answer: $3$. The average rate of change is the slope between the points, calculated as rise over run.

Flashcard 21: A pie chart shows $40\%$ of a budget is rent. What fraction of the budget is rent in simplest form?

Answer: $\frac{2}{5}$. Simplifying 40/100 by dividing numerator and denominator by 20 produces the fraction in lowest terms.

Flashcard 22: Identify the independent variable on a standard graph where $x$ is time and $y$ is distance.

Answer: Time (the $x$-variable). The independent variable, typically time on the x-axis, does not depend on other factors in the relationship.

Flashcard 23: What does the domain of a graph's $x$-values mean for the data shown?

Answer: All input values $x$ for which the graph has points. The domain includes all input values for which the function is defined and produces outputs on the graph.

Flashcard 24: A table shows $(x,y)$ pairs: $(1,3)$, $(2,6)$, $(3,9)$. What is $y$ when $x=4$?

Answer: $12$. The pattern y=3x extends linearly to predict the value at x=4.

Flashcard 25: Find the slope between $( -1,4)$ and $(3,-8)$.

Answer: $m=-3$. The slope formula yields a change in y of -12 divided by a change in x of 4.