Relations and Functions in Algebra Class 10

A set of ordered pairs, typically represented as (x,y) that shows a relationship between two variables.

A special type of relation where each input (x-value) has exactly one output (y-value).

A function whose graph is a straight line.

The rate at which the output (y-value) changes for every unit change in the input (x-value).

The point where the line crosses the y-axis. Usually the point (0, y) where x = 0.

A representation of a linear function which indicates the slope and y-intercept. The general form is y = mx + c where m is the slope and c is the y-intercept.

A visual representation of a relationship showing data points and a line that best fits them.

A line drawn through the center of a scatter plot to show the general trend of the data. It represents an approximation of the relationship between the variables involved. The line is drawn so that the distance between its points to those on the plot is minimized.

A method of finding a line of best fit by drawing a line that minimizes the sum of the squared distances from each data point to the line.

The ability of a mathematical function to accurately predict the output based on the input.

A measure of the strength and direction of a linear relationship between two variables, ranging from -1 to 1.

A relationship between two variables that has a positive correlation coefficient (r) where both variables change in the same direction.

A relationship between two variables that has a negative correlation coefficient (r) where the variables change in opposite directions.

A situation where two variables have no clear relationship, often because of chance.

Drawing conclusions about the nature of a relationship between data points based on visual inspection, especially when dealing with a scatter plot.

This is a way to represent data graphically, where the data points are distinct and separate.

This is a way to represent data graphically, where the data points are connected and can take on any value within a given range.

The rate of change measures how much a quantity changes over a specific interval. In a graph, it's the slope of a line!

Linear relationships have a constant rate of change, creating a straight line on the graph.

The x-intercept is the point where the graph crosses the x-axis (where y = 0). The y-intercept is the point where the graph crosses the y-axis (where x = 0).

This is a way to write the equation of a line, using the point-slope form (y - y1 = m(x - x1)), where 'm' is the slope and (x1, y1) is a point on the line.

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are integers and A is a whole number (not a fraction or negative).