ISEE Middle Level Quantitative Reasoning Flashcards: Interpreting Graphs And Tables

What this deck covers

This deck focuses on Interpreting Graphs And Tables, giving you a quick way to review the definitions, rules, and examples that matter most for ISEE Middle Level Quantitative Reasoning.

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: A table shows $(x,y)$ pairs: $(1,4)$, $(2,6)$, $(3,8)$. What is $y$ when $x=5$?

Answer: $12$. The pattern shows a linear relationship with slope 2 and y-intercept 2, so for $x=5$, $y=2(5)+2=12$.

Flashcard 2: What does the $x$-axis represent on most graphs?

Answer: The independent variable (input). In standard coordinate graphs, the horizontal x-axis displays the independent variable, which is manipulated or input to observe changes in the dependent variable.

Flashcard 3: What does the $y$-axis represent on most graphs?

Answer: The dependent variable (output). The vertical y-axis on graphs typically plots the dependent variable, which responds to or is affected by changes in the independent variable.

Flashcard 4: What is the meaning of the ordered pair $(x,y)$ on a coordinate graph?

Answer: At input $x$, the output is $y$. An ordered pair $(x,y)$ indicates a specific point where the input value $x$ corresponds to the output value $y$ in the relationship being graphed.

Flashcard 5: Identify whether the relationship is proportional if points include $(0,3)$ and $(2,6)$.

Answer: Not proportional (does not pass through $(0,0)$). A proportional relationship requires passing through (0,0), but here y=3 at x=0, so it is not proportional.

Flashcard 6: A scatter plot shows points close to a rising line from left to right. What correlation is shown?

Answer: Positive correlation. Points clustering around an upward-trending line indicate that as one variable increases, the other tends to increase, showing positive correlation.

Flashcard 7: 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 calculates the rate of change as the difference in $y$-values divided by the difference in $x$-values between two points.

Flashcard 8: Identify the slope of a horizontal line on a graph.

Answer: Slope $0$. A horizontal line has no vertical change, resulting in a slope of zero when applying the slope formula.

Flashcard 9: Identify the slope of a vertical line on a graph.

Answer: Undefined slope. A vertical line has no horizontal change, leading to division by zero in the slope formula, which is undefined.

Flashcard 10: What does a positive slope indicate about how $y$ changes as $x$ increases?

Answer: $y$ increases as $x$ increases. A positive slope means the line rises from left to right, showing that the dependent variable increases with the independent variable.

Flashcard 11: What does a negative slope indicate about how $y$ changes as $x$ increases?

Answer: $y$ decreases as $x$ increases. A negative slope means the line falls from left to right, indicating that the dependent variable decreases as the independent variable increases.

Flashcard 12: What is the $y$-intercept of a graph in terms of an ordered pair?

Answer: The point where $x=0$. The y-intercept is the point where the graph crosses the y-axis, occurring when the independent variable $x$ is zero.

Flashcard 13: What is the $x$-intercept of a graph in terms of an ordered pair?

Answer: The point where $y=0$. The x-intercept is the point where the graph crosses the x-axis, occurring when the dependent variable $y$ is zero.

Flashcard 14: Find the slope between $(2,5)$ and $(6,13)$.

Answer: $2$. Using the slope formula, $(13-5)/(6-2) = 8/4 = 2$, confirming the rate of change between the points.

Flashcard 15: Find the slope between $(1,7)$ and $(4,1)$.

Answer: $-2$. Applying the slope formula gives $(1-7)/(4-1) = -6/3 = -2$, showing the negative rate of change.

Flashcard 16: A line passes through $(0,3)$ and $(2,7)$. What is its slope?

Answer: $2$. The slope is calculated as $(7-3)/(2-0) = 4/2 = 2$, representing the constant rate of change for the line.

Flashcard 17: A line has slope $-3$ and passes through $(0,4)$. What is $y$ when $x=2$?

Answer: $-2$. Using $y = -3x + 4$, substitute $x=2$ to get $y = -6 + 4 = -2$, following the line equation.

Flashcard 18: A table shows $(x,y)$ pairs: $(0,10)$, $(1,7)$, $(2,4)$. What is the rate of change?

Answer: $-3$ per $1$ unit of $x$. The consistent decrease of 3 in $y$ for each increase of 1 in $x$ indicates a constant rate of change of -3.

Flashcard 19: In a table, $y$ increases by $15$ when $x$ increases by $3$. What is the unit rate?

Answer: $5$ per $1$ unit of $x$. The unit rate is the change in $y$ divided by the change in $x$, so $15/3=5$ per unit increase in $x$.

Flashcard 20: Which option is the best estimate if a graph’s scale is $5$ units per tick and the point is $3$ ticks up?

Answer: $15$ units. Multiplying the number of ticks by the scale per tick gives $3 \times 5 = 15$, estimating the value on the graph.

Flashcard 21: A bar chart shows Category A $=12$ and Category B $=18$. What is the difference $B-A$?

Answer: $6$. Subtracting the values directly from the bar chart gives $18 - 12 = 6$, representing the difference between categories.

Flashcard 22: A line graph shows a value of $20$ at $t=2$ and $26$ at $t=5$. What is the average change per unit $t$?

Answer: $2$ per unit $t$. The average rate is the total change in value divided by the change in $t$, so $(26-20)/(5-2) = 6/3 = 2$.

Flashcard 23: A pie chart shows $25\%$ of a group of $80$ students. How many students is that?

Answer: $20$ students. Calculating $25\%$ of 80 as $0.25 \times 80 = 20$ determines the portion represented in the pie chart.

Flashcard 24: A pie chart shows $40\%$ of $150$ items are defective. How many are defective?

Answer: $60$. Converting $40\%$ to 0.4 and multiplying by 150 gives $0.4 \times 150 = 60$, quantifying the defective items.

Flashcard 25: A table lists $x: 2,4,6$ and $y: 5,10,15$. What is the constant of proportionality $k$ in $y=kx$?

Answer: $\frac{5}{2}$. Dividing $y$ by $x$ for each pair yields $5/2 = 10/4 = 15/6 = \frac{5}{2}$, the constant $k$ in direct proportion.