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.

Front

What does the rate of change represent in a linear equation?

Back

The rate of change represents how much the dependent variable (y) changes for a unit change in the independent variable (x).

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

What does the slope of a line indicate?

Back

The slope indicates the steepness of the line and the direction of the relationship between the variables.

Front

What is the y-intercept in a linear equation?

Back

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

Front

What does it mean for a relationship to be proportional?

Back

A proportional relationship means that the ratio between the two variables is constant, and the line passes through the origin (0,0).

Front

How can you identify a proportional relationship from a table of values?

Back

A proportional relationship can be identified if the ratio of y to x is the same for all pairs of values.

Front

What is the significance of the point (0,0) in a proportional relationship?

Back

The point (0,0) indicates that when the independent variable (x) is zero, the dependent variable (y) is also zero.

Front

What does it mean if a linear equation has a negative slope?

Back

A negative slope indicates that as the independent variable (x) increases, the dependent variable (y) decreases.

Front

What is the difference between a linear equation and a nonlinear equation?

Back

A linear equation represents a straight line, while a nonlinear equation represents a curve.