Linear Relationships - 4 Corners Activity

Front

What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph. It can be described by a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is and the direction it goes (upward or downward).

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is the value of y when x is 0, represented by the 'b' in the equation y = mx + b.

Front

What is the difference between a table and a graph in representing linear relationships?

Back

A table organizes data in rows and columns, showing the relationship between variables numerically, while a graph visually represents the relationship, allowing for easier interpretation of trends and patterns.

Front

What is an equation of a line?

Back

An equation of a line is a mathematical statement that describes the relationship between the x and y coordinates of points on the line, typically in the form y = mx + b.

Front

How can you identify a linear relationship from a set of data points?

Back

You can identify a linear relationship by plotting the data points on a graph. If the points form a straight line or close to a straight line, the relationship is linear.

Front

What does it mean for a description to be incorrect in the context of linear relationships?

Back

An incorrect description may misrepresent the relationship, such as stating the wrong cost per item or the wrong rate of change, which can lead to misunderstandings of the linear relationship.

Front

What is the significance of the term 'ascend' in a linear relationship context?

Back

'Ascend' refers to an increase in value, indicating that as one variable increases, the other variable also increases, which is represented by a positive slope in a linear relationship.

Front

What is the role of a graph in understanding linear relationships?

Back

A graph provides a visual representation of the relationship between variables, making it easier to see trends, slopes, and intercepts, and to understand how changes in one variable affect another.

Front

What does it mean for a graph to not belong in a set of representations of linear relationships?

Back

It means that the graph does not accurately represent the linear relationship described by the equation or table, possibly due to being nonlinear or misrepresenting the data.