3.1 Rate of Change and Slope

Front

What is the definition of slope in a linear function?

Back

The slope of a linear function is a measure of the steepness of the line, calculated as the change in the y-coordinate divided by the change in the x-coordinate (rise over run).

Front

How do you determine if a function is linear?

Back

A function is linear if it can be represented by a straight line on a graph, meaning it has a constant rate of change and can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

The slope (m) is calculated using the formula: 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 it does not have a defined angle of inclination and the x-coordinates of the points are the same.

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates that the line is horizontal, meaning there is no change in the y-coordinate as the x-coordinate changes.

Front

If a line passes through the points (2, 4) and (6, 12), what is the slope?

Back

The slope is 2, calculated as m = (12 - 4) / (6 - 2) = 8 / 4 = 2.

Front

What is the rate of change in a linear function?

Back

The rate of change in a linear function is the same as the slope, representing how much the output (y) changes for a unit change in the input (x).

Front

How can you identify a nonlinear function from its graph?

Back

A nonlinear function will not form a straight line on a graph; it may curve or have varying slopes at different points.

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

If a line has a slope of -5/4, what does this indicate about its direction?

Back

A slope of -5/4 indicates that the line descends from left to right, meaning as x increases, y decreases.