Interpreting Graphs and Tables - SSAT Upper Level Quantitative

1. If a line passes through $(2,3)$ and $(6,11)$, what is its slope?

   $2$. Slope is found using the formula $\frac{y_2 - y_1}{x_2 - x_1}$ applied to the given points.

2. A scatter plot trend is upward from left to right. What correlation sign does this suggest?

   Positive correlation. An upward trend in a scatter plot indicates that as one variable increases, the other tends to increase, suggesting positive correlation.

3. Identify the independent variable on a standard graph with labeled axes.

   The variable on the $x$-axis. In standard graphing conventions, the independent variable is plotted on the horizontal x-axis as it is manipulated or controlled.

4. A table shows $x=1,2,3$ with $y=2,4,6$. What is the constant rate of change?

   $2$ per $1$ unit of $x$. The constant rate of change is the consistent increase in y for each unit increase in x, as shown in the table.

5. Find the mean of the table values $3,6,9$.

   $6$. The mean is calculated by summing all values and dividing by the number of values in the set.

6. What does it mean if a line graph is horizontal over an interval of $x$?

   The value of $y$ is constant on that interval. A horizontal line segment signifies no change in the dependent variable despite variations in the independent variable over that period.

7. If a line has slope $-3$ and passes through $(0,5)$, what is $y$ when $x=2$?

   $-1$. Using the line equation $y = mx + b$ with given slope and y-intercept, substitute x=2 to find y.

8. A graph point is labeled $(4,9)$. What is the value of $y$ when $x=4$?

   $9$. In a coordinate pair (x, y), the second number directly gives the y-value for the specified x.

9. A scatter plot trend is downward from left to right. What correlation sign does this suggest?

   Negative correlation. A downward trend in a scatter plot shows that as one variable increases, the other decreases, indicating negative correlation.

10. A line graph shows $y$ increases from $10$ to $16$ while $x$ increases from $2$ to $5$. Find slope.

    $2$. Slope is computed as the change in y divided by the change in x over the given interval.

11. A table lists $x=0,1,2$ with $y=5,8,11$. What is the $y$-intercept?

    $5$. The y-intercept is the y-value corresponding to x=0 in the linear relationship depicted in the table.

12. What does a positive slope on a line graph indicate about the relationship between $x$ and $y$?

    As $x$ increases, $y$ increases. A positive slope indicates a direct relationship where the dependent variable increases proportionally with the independent variable.

13. What is the range of a data set shown on a graph or in a table?

    Maximum value minus minimum value. The range measures the spread of data by subtracting the smallest value from the largest in the set.

14. A table gives total cost $C$ for $n$ items: $(n,C)=(2,10),(5,25)$. What is the unit cost $\frac{C}{n}$?

    $5$. The unit cost is the constant ratio of total cost to number of items, verified as consistent across table entries.

15. Find the range of the table values $4,10,1,7$.

    $9$. The range is determined by subtracting the minimum value from the maximum value in the data set.

16. A pie chart shows $40\%$ for $A$. What fraction of the whole is category $A$?

    $\frac{2}{5}$. Convert the percentage to a fraction by dividing by 100 and simplifying to lowest terms.

17. What is the average rate of change from $x=a$ to $x=b$ on a graph?

    $\frac{f(b)-f(a)}{b-a}$. The average rate of change is computed as the difference in function values divided by the difference in x-values over the interval.

18. Identify the dependent variable on a standard graph with labeled axes.

    The variable on the $y$-axis. The dependent variable, which responds to changes in the independent variable, is conventionally placed on the vertical y-axis.

19. What does the slope between two points $(x_1,y_1)$ and $(x_2,y_2)$ represent on a line graph?

    Rate of change: $\frac{y_2-y_1}{x_2-x_1}$. The slope formula calculates the rate of change in the dependent variable per unit change in the independent variable between two points on the graph.

20. What does a negative slope on a line graph indicate about the relationship between $x$ and $y$?

    As $x$ increases, $y$ decreases. A negative slope shows an inverse relationship where the dependent variable decreases as the independent variable increases.

21. What is the median of the values $2,5,7,9,12$ (as might appear in a table column)?

    $7$. For an odd number of sorted values, the median is the middle value in the ordered list.

22. What is the meaning of the $y$-intercept of a line graph in context?

    The value of $y$ when $x=0$. The y-intercept indicates the initial value of the dependent variable when the independent variable is at its starting point of zero.

23. A bar chart shows counts $A=12$, $B=9$, $C=15$. Which category is greatest?

    $C$. The greatest category in a bar chart is identified by comparing the heights of the bars representing each count.

24. If a graph uses a scale of $2$ units per tick mark, what value is $3$ ticks above $0$ on that axis?

    $6$. Multiply the number of tick marks by the scale value per tick to find the distance from zero.

25. A pie chart shows $25\%$ for a category. What central angle (in degrees) represents it?

    $90^\circ$. The central angle is calculated as the percentage times 360 degrees, the total degrees in a circle.

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