Linear Functions and Slope Concepts

Front

What is a linear function?

Back

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the function. It indicates how much the y-value changes for a unit change in the x-value.

Front

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

Back

Front

What is the y-intercept of a linear function?

Back

Front

What does it mean if a function is increasing?

Back

A function is increasing if, as the x-values increase, the y-values also increase. This is indicated by a positive slope.

Front

What does it mean if a function is decreasing?

Back

A function is decreasing if, as the x-values increase, the y-values decrease. This is indicated by a negative slope.

Front

What is the average rate of change of a function?

Back

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating that there is no change in the y-value as the x-value changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x-value is 0, leading to division by zero in the slope formula.

Front

If a line has a slope of 1, what does this indicate?

Back

A slope of 1 indicates that for every unit increase in x, the y-value also increases by the same amount, resulting in a 45-degree angle with the x-axis.