Multiple Representations of 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, where the rate of change is constant.

Front

What does it mean when a graph is nonlinear?

Back

A nonlinear graph indicates that the rate of change between the variables is not constant, meaning the relationship cannot be represented by a straight line.

Front

What is slope-intercept form?

Back

Slope-intercept form is a way of writing the equation of a line as y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you identify the slope from the equation y = mx + b?

Back

The slope is the coefficient of x (m) in the equation y = mx + b.

Front

What is the y-intercept in the equation y = mx + b?

Back

The y-intercept is the value of y when x is 0, represented by b in the equation y = mx + b.

Front

What does a positive slope indicate about a linear relationship?

Back

A positive slope indicates that as x increases, y also increases, showing a direct relationship.

Front

What does a negative slope indicate about a linear relationship?

Back

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

Front

How can you graph the equation y = 2x - 3?

Back

To graph y = 2x - 3, start at the y-intercept (0, -3) and use the slope (2) to find another point by going up 2 units and right 1 unit.

Front

What is the slope of the line represented by the equation y = -2/5 x + 2?

Back

The slope of the line is -2/5.

Front

What is the y-intercept of the line represented by the equation y = -2/5 x + 2?

Back

The y-intercept of the line is 2.