Chapter 7 Math Vocab
form
(of an association) The form of an association can be linear or non-linear. The form can contain cluster of data. A residual plot can help determine if a particular form is appropriate for modeling the relationship.
strength (of an association)
A description of how much scatter there is in the data away from the line or curve of best fit.
negative slope
A line has negative slope if it slopes downward from left to right on a graph.
positive slope
A line has positive slope if it slopes upward from left to right on a graph. See slope.
line of best fit
A line of best fit shows a trend in the data representing where the data falls. This line does not need to touch any of the actual data points. Instead, it shows where the data generally falls. The line is a mathematical model of the data.
outlier
A number in a set of data that is much larger or much smaller than the other numbers in the set.
unit rate
A rate with a denominator of one when simplified.
central angle
An angle with its vertex at the center of a circle.
cluster
An association (relationship) between two numerical variables can be described by its form, direction, strength, and outliers. When data seems to be "gathered" around a particular value.
linear equation
An equation in two variables whose graph is a line. For example, y = 2.1x − 8 is a linear equation. The standard form for a linear equation is ax + by = c, where a, b, and c are constants and a and b are not both zero. Most linear equations can be written in y = mx + b form, which is more useful for determining the line's slope and y-intercept
constant of proportionality
the constant value of the ratio of two proportional quantities x and y; usually written y = kx, where k is the factor of proportionality
slope
A ratio that describes how steep (or flat) a line is. Slope can be positive, negative, or even zero, but a straight line has only one slope. Slope is the ratio pic or pic, sometimes written pic. When the equation of a line is written in y = mx + b form, m is the slope of the line. Some texts refer to slope as the ratio of the "rise over the run." A line has positive slope if it slopes upward from left to right on a graph, negative slope if it slopes downward from left to right, zero slope if it is horizontal, and undefined slope if it is vertical. lope is interpreted in context as the amount of change in the y-variable for an increase of one unit in the x-variable.
association
A relationship between two (or more) variables. An association between numerical variables can be displayed on a scatterplot, and described by its form, direction, strength, and outliers. Possible association between two categorical variables can be studied in a relative frequency table. Also see scatterplot.
frequency table
A table that displays counts, or frequencies, of data.
circle graph
A way of displaying data that can be put into categories (like what color you prefer, your gender, or the state you were born in). A circle graph shows the proportion each category is of the whole.
negative association
If one variable decreases as the other variable increases, there is said to be a negative association.
positive association
If one variable in a relationship increases as the other variable increases, the direction is said to be a positive association.
categorical variable
In previous lessons, you described the association between two numerical variables, such as the amount of fertilizer used and the height of the plant. Some variables, however - such as gender, eye color, names of countries, or weather conditions - are not numerical. Since the data are in categories, non-numerical variables are called categorical variables. Another type of categorical variable occurs when numerical variables are lumped into categories, such as in age groups.
simple interest
Interest paid on the principal alone.
y-intercept
The point(s) where a graph intersects the y-axis. A function has at most one y-intercept; a relation may have several. The y-intercept of a graph is important because it often represents the starting value of a quantity in a real-world situation. For example, on the graph of a tile pattern the y-intercept represents the number of tiles in Figure 0. We sometimes report the y-intercept of a graph with a coordinate pair, but since the x-coordinate is always zero, we often just give the y-coordinate of the y-intercept. For example, we might say that the y-intercept of the graph below is (0, 2), or we might just say that the y-intercept is 2. When a linear equation is written in y = mx + b form, b tells us the y-intercept of the graph. For example, the equation of the graph below is y = x + 2 and its y-intercept is 2.
lattice points
The points on a coordinate grid where the grid lines intersect. The diagram below shows two lattice points. The coordinates of lattice points are integers.
y = mx + b
When two quantities x and y have a linear relationship, that relationship can be represented with an equation in y = mx + b form. The constant m is the slope, and b is the y-intercept of the graph. For example, the graph below shows the line represented by the equation y = 2x + 3, which has a slope of 2 and a y-intercept of 3. This form of a linear equation is also called the slope-intercept form.