Different 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. It can be described by a linear 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 in a linear relationship?

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 unit change in x.

Front

How do you determine the steepness of a line on a graph?

Back

The steepness of a line is determined by its slope. A steeper line has a greater absolute value of slope, indicating a greater rate of change.

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 is the value of y when x is 0, represented by the term 'b' in the equation y = mx + b.

Front

How can you compare the rates of change of two linear equations?

Back

You can compare the rates of change by looking at the slopes of the equations. The equation with the greater slope has a greater rate of change.

Front

What does it mean if two lines are parallel in terms of their slopes?

Back

If two lines are parallel, they have the same slope, which means they have the same rate of change.

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does a negative slope indicate about a linear relationship?

Back

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

Front

What is the significance of the point (0, b) in a linear equation?

Back

The point (0, b) represents the y-intercept of the line, where the line crosses the y-axis.

Front

How can you find the starting point of a linear relationship from a graph?

Back

The starting point can be found by identifying the y-intercept, which is the value of y when x is 0.