Linear Relationships

Front

What is the slope in the equation y=mx + b?

Back

The slope (m) represents the rate of change of y with respect to x.

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the value of y when x=0, indicating where the line crosses the y-axis.

Front

What is the equation for a linear relationship?

Back

A linear relationship can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you determine the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

What does it mean if a graph is linear?

Back

A graph is linear if it forms a straight line, indicating a constant rate of change.

Front

What is a proportional relationship?

Back

A proportional relationship is a linear relationship that passes through the origin (0,0).

Front

If the slope of a line is negative, what does that indicate about the relationship between x and y?

Back

A negative slope indicates that as x increases, y decreases.

Front

What is the significance of the delivery fee in a linear cost equation?

Back

The delivery fee represents the fixed cost (y-intercept) that does not change with the number of people (x).

Front

How can you identify the y-intercept from a graph?

Back

The y-intercept can be identified as the point where the line crosses the y-axis.

Front

What does the term 'rate of change' refer to in linear relationships?

Back

The rate of change refers to how much y changes for a unit change in x, represented by the slope.