Linear Relationships

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 shows how one variable changes in relation to another.

Front

What are independent and dependent quantities?

Back

Independent quantities are the variables that can be changed or controlled in an experiment (e.g., amount of fertilizer). Dependent quantities are the variables that are measured or observed (e.g., height of plants).

Front

What is the equation of a line in slope-intercept form?

Back

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you identify the dependent quantity from a table?

Back

The dependent quantity is usually the one that changes in response to the independent quantity. It is often found in the second column of a table.

Front

What does the slope of a line represent in a linear relationship?

Back

The slope of a line represents the rate of change between the independent and dependent quantities. It shows how much the dependent variable changes for each unit change in the independent variable.

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 represents the value of the dependent variable when the independent variable is zero.

Front

How can you represent a real-world situation with a linear equation?

Back

You can represent a real-world situation with a linear equation by identifying the independent and dependent variables, determining the slope, and finding the y-intercept based on the context.

Front

What is a function in mathematics?

Back

A function is a relationship between two sets of values where each input (independent variable) has exactly one output (dependent variable).

Front

How do you graph a linear equation?

Back

To graph a linear equation, you can plot the y-intercept on the y-axis, use the slope to find another point, and then draw a straight line through the points.

Front

What is the difference between a positive and negative slope?

Back

A positive slope indicates that as the independent variable increases, the dependent variable also increases. A negative slope indicates that as the independent variable increases, the dependent variable decreases.