Pre Algebra Chapter 8

Rise over run is a mathematical term used to describe the steepness of a line. It represents the vertical change (rise) divided by the horizontal change (run) between two points on the line. This value is commonly referred to as the slope of the line.

The correct answer is "slope" because the slope of a line is a measure of its tilt or steepness. It is the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. A positive slope indicates an upward tilt, a negative slope indicates a downward tilt, and a slope of zero indicates a horizontal line. Therefore, slope is the appropriate ratio that describes the tilt of a line.

The x-coordinate of a relation refers to the set of all possible input values or independent variables. It represents the values that can be substituted into the relation to determine the corresponding y-coordinate or output values. The x-coordinate is commonly referred to as the domain of the relation, which defines the range of valid input values. Therefore, the correct answer is "domain."

The four kinds of slopes are positive, negative, zero, and undefined. A positive slope indicates that the line is increasing from left to right, while a negative slope indicates that the line is decreasing. A slope of zero means that the line is horizontal and has no incline. An undefined slope occurs when the line is vertical and has no defined incline.

In the slope-intercept form, the variable "m" represents the slope of the line, while the variable "b" represents the y-intercept. The slope is a measure of how steep the line is, while the y-intercept is the point where the line intersects the y-axis. Therefore, in the given answer, "m" correctly represents the slope and "b" correctly represents the y-intercept.

The slope-intercept form is a linear equation in the form y=mx+b, where m represents the slope of the line and b represents the y-intercept. In this form, it is easy to identify the slope and y-intercept of a line by simply looking at the equation. The slope-intercept form is commonly used in mathematics and physics to represent linear relationships between variables.

The y-coordinate of a relation refers to the set of all possible values that the dependent variable (y) can take on. This set is known as the range of the relation. In other words, the range represents the output values of the relation, which are determined by the corresponding input values (x-coordinate). Therefore, the correct answer for the y-coordinate of a relation is the range.

A set of ordered pairs refers to a collection of pairs of elements where the order of the elements in each pair is important. This collection is known as a relation. In a relation, each ordered pair consists of two elements, usually represented as (x, y), where x is the first element and y is the second element. Relations are commonly used in mathematics to establish connections or associations between different elements or objects.

A one-to-one relationship refers to a situation where each element in one set is uniquely associated with an element in another set. In the context of functions, a one-to-one relationship means that for every input value, there is only one unique output value. This ensures that no two different input values will produce the same output value. It can also be described as an injective function, where no two elements in the domain map to the same element in the co-domain.