Slope Flashcard Review

Front

What is the definition of slope in a linear function?

Back

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

Front

How do you 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.

Front

What is the slope of a horizontal line?

Back

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

Front

If a line has a slope of 2, what does this mean in terms of rise and run?

Back

A slope of 2 means that for every 1 unit you move to the right (run), the line rises 2 units (rise).

Front

What is the slope of the line represented by the equation y = 3x + 1?

Back

The slope of the line is 3, which is the coefficient of x in the equation.

Front

How can you determine the slope from a graph?

Back

To determine the slope from a graph, select two points on the line, calculate the rise (change in y) and run (change in x), and then use the formula slope = rise/run.

Front

What is the slope of the line that passes through the points (2, 3) and (4, 7)?

Back

The slope is 2, calculated as (7 - 3) / (4 - 2).

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that the line descends from left to right, meaning as the x-value increases, the y-value decreases.

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 given change in the input (x).