Slope Flashcard

Front

What is the definition of slope in a linear function?

Back

The slope is the ratio of the change in the y-coordinate to the change in the x-coordinate between two points on a line.

Front

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

Back

Slope (m) = (y2 - y1) / (x2 - x1)

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates that the line is vertical, meaning there is no change in the x-coordinate.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

What is the rate of change in a linear function?

Back

The rate of change is the same as the slope; it represents how much y changes for a unit change in x.

Front

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

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does a positive slope indicate about the direction of a line?

Back

A positive slope indicates that the line rises from left to right.

Front

What does a negative slope indicate about the direction of a line?

Back

A negative slope indicates that the line falls from left to right.

Front

What is the significance of the y-intercept in a linear equation?

Back

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

Front

How can you determine if a function is linear or nonlinear from a table of values?

Back

A function is linear if the rate of change (slope) between any two points is constant; otherwise, it is nonlinear.