Enhance Your Learning with Linear Functions and Graphs Flash Cards for quick understanding
The measure of the steepness of a line. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.
The points where a line crosses the x-axis (x-intercept) or the y-axis (y-intercept). They can be found by setting one of the variables to zero and solving for the other variable.
Mathematical representations of lines. They can be written in various forms, including slope-intercept form, point-slope form, and standard form.
Plotting points and connecting them to form a line on a coordinate plane based on the given equation of the line.
Parallel lines have the same slope and will never intersect. Perpendicular lines have slopes that are negative reciprocals of each other and intersect at a right angle.
An equation of a line in the form y = mx + b, where m represents the slope and b represents the y-intercept.
An equation of a line in the form y - y₁ = m(x - x₁), where m represents the slope and (x₁, y₁) represents a point on the line.
An equation of a line in the form Ax + By = C, where A, B, and C are constants and A and B are not both zero.
Inequalities that involve linear expressions. The solution set is the region on the coordinate plane that satisfies the inequality.
A set of two or more linear equations with the same variables. The solution is the point(s) where the lines intersect.
Real-world problems that can be modeled using linear functions, such as distance-time relationships, cost-profit analysis, and population growth.
Modifying the graph of a linear function by shifting, stretching, or reflecting it. This changes the slope, intercepts, or both.
Functions that are defined by different equations for different intervals or pieces of the domain. Each piece is a linear function.
A statistical method used to find the best-fitting line that represents the relationship between two variables. It is often used for trend analysis and prediction.
Mathematical representations of real-world situations using linear functions. They can be used to make predictions and analyze data.
The set of all possible input values (x-values) of a function or relation.
The set of all possible output values (y-values) of a function or relation.
A way to represent a function using symbols. It typically involves using f(x) to represent the output (y-value) corresponding to a given input (x-value).
A test used to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, the graph is not a function.
The x-coordinate of the point where a graph intersects the x-axis. It is the value of x when y is equal to zero.
The y-coordinate of the point where a graph intersects the y-axis. It is the value of y when x is equal to zero.
A slope that goes uphill from left to right. It indicates a positive relationship between the variables.
A slope that goes downhill from left to right. It indicates a negative relationship between the variables.
A slope of zero, which means the line is horizontal. It indicates no change in the y-value for any change in the x-value.
A slope that is not defined, which means the line is vertical. It indicates no change in the x-value for any change in the y-value.
A relationship between two variables where one variable is a constant multiple of the other. It can be represented by a linear equation in the form y = kx, where k is the constant of variation.
A relationship between two variables where the product of the variables is a constant. It can be represented by a linear equation in the form xy = k, where k is the constant of variation.
A sequence of numbers in which the difference between consecutive terms is constant. It can be represented by a linear equation in the form an = a₁ + (n - 1)d, where a₁ is the first term and d is the common difference.
A sequence of numbers in which the ratio between consecutive terms is constant. It can be represented by a linear equation in the form an = a₁ * r^(n - 1), where a₁ is the first term and r is the common ratio.
Lines in the same plane that never intersect. They have the same slope.
Lines that intersect at a right angle. They have slopes that are negative reciprocals of each other.
An equation of a line in the form Ax + By = C, where A, B, and C are constants and A and B are not both zero.
An equation of a line in the form y - y₁ = m(x - x₁), where m represents the slope and (x₁, y₁) represents a point on the line.
An equation of a line in the form y = mx + b, where m represents the slope and b represents the y-intercept.
The set of all possible input values (x-values) for which the function is defined.
The set of all possible output values (y-values) that the function can produce.
An inequality that involves a linear expression. The solution set is the region on the coordinate plane that satisfies the inequality.
A set of two or more linear equations with the same variables. The solution is the point(s) where the lines intersect.
A function that can be represented by a straight line. It has a constant rate of change and a linear equation.
A mathematical representation of a real-world situation using a linear function. It can be used to make predictions and analyze data.
A function that is defined by different equations for different intervals or pieces of the domain. Each piece is a linear function.
Modifying the graph of a linear function by shifting, stretching, or reflecting it. This changes the slope, intercepts, or both.
An equation that represents a straight line when graphed. It can be written in various forms, such as slope-intercept form, point-slope form, or standard form.
A way to represent a linear function using symbols. It typically involves using f(x) to represent the output (y-value) corresponding to a given input (x-value).
The visual representation of a linear function on a coordinate plane. It is a straight line that passes through two points or has a specific slope and y-intercept.
A table that shows the input (x-values) and output (y-values) of a linear function. It can be used to find patterns and graph the function.
The equation or expression that defines a linear function. It relates the input (x-value) to the output (y-value) using mathematical operations.
The constant rate at which the output (y-value) changes with respect to the input (x-value) in a linear function. It is equal to the slope of the line.
The point(s) where a linear function crosses the x-axis (x-intercept) or the y-axis (y-intercept). They can be found by setting one of the variables to zero and solving for the other variable.
The set of all possible input values (x-values) for which the linear function is defined.
The set of all possible output values (y-values) that the linear function can produce.
The measure of the steepness of a linear function. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.
An equation of a linear function in the form x/a + y/b = 1, where a and b are the x-intercept and y-intercept, respectively.
An equation of a linear function in the form Ax + By = C, where A, B, and C are constants and A and B are not both zero.
An equation of a linear function in the form y = mx + b, where m represents the slope and b represents the y-intercept.
An equation of a linear function in the form y - y₁ = m(x - x₁), where m represents the slope and (x₁, y₁) represents a point on the line.
A test used to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, the graph is not a function.
The x-coordinate of the point where a linear function intersects the x-axis. It is the value of x when y is equal to zero.
The y-coordinate of the point where a linear function intersects the y-axis. It is the value of y when x is equal to zero.