Understanding Linear Relationships and Equations

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 an 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 much y changes for a one-unit increase in x.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

What does the equation y = x/2.5 represent?

Back

This equation represents a multiplicative relationship where y is directly proportional to x, with a constant of proportionality of 1/2.5.

Front

What does the equation y = x + 5 indicate?

Back

This equation indicates an additive relationship where the value of y is always 5 more than the value of x.

Front

How can you describe the relationship between fluid ounces and sports drinks if there are 28 fluid ounces in each bottle?

Back

The relationship can be described as: The fluid ounces (f) are 28 times the number of drinks (d), or f = 28d.

Front

What does the equation y = 6x mean in a real-world context?

Back

In this context, it means that the amount of money Tori has (y) is 6 times the amount of money her sister has (x).

Front

What is the difference between dependent and independent variables?

Back

The independent variable is the one that is changed or controlled in an experiment, while the dependent variable is the one that is measured or affected.

Front

What is an additive relationship?

Back

An additive relationship is when one quantity is increased or decreased by a constant amount, represented by an equation of the form y = x + b.

Front

What is a multiplicative relationship?

Back

A multiplicative relationship is when one quantity is multiplied by a constant factor, represented by an equation of the form y = kx, where k is a constant.