MathVocab

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.

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.

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.

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.

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.