Linear Relationships

Front

What does the 'm' represent in the equation y = mx + b?

Back

The 'm' represents the slope of the line, indicating the rate of change of y with respect to x.

Front

What does the 'b' represent in the equation y = mx + b?

Back

The 'b' represents the y-intercept, which is the point where the line crosses the y-axis.

Front

What is a linear relationship?

Back

A linear relationship is one that produces a straight line when graphed.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates how steep the line is and the direction of the relationship between the variables.

Front

What does it mean for a graph to show a proportional relationship?

Back

A graph shows a proportional relationship if it passes through the origin (0,0).

Front

What is the definition of a coordinate system?

Back

A coordinate system is a system that uses numbers to uniquely determine the position of a point or other geometric element.

Front

What is the difference between a linear equation and a non-linear equation?

Back

A linear equation produces a straight line when graphed, while a non-linear equation produces a curve.

Front

How can you determine the slope from two points on a line?

Back

The slope can be determined using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What is the formula for the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is y = mx + b.

Front

What does it mean if the slope of a line is negative?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship.