Slope

Front

What is the definition of slope in mathematics?

Back

Slope is a measure of the steepness or incline of a line, typically represented as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

How do you calculate the slope of a line using two points?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates that the line is vertical, meaning it goes straight up and down, and there is no horizontal change.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating that there is no vertical change as you move along the line.

Front

If a line has a slope of -3/2, what does this indicate about its direction?

Back

A slope of -3/2 indicates that the line descends from left to right, meaning for every 2 units you move to the right, the line moves down 3 units.

Front

What is the slope of a line that rises 4 units for every 5 units it runs?

Back

The slope of the line is 4/5.

Front

How can you determine the slope from a graph?

Back

To determine the slope from a graph, identify two points on the line, calculate the rise (vertical change) and run (horizontal change) between those points, and then use the formula slope = rise/run.

Front

What is the slope of the line represented by the equation y = 2x + 3?

Back

The slope of the line is 2, which is the coefficient of x in the equation.

Front

What does a positive slope indicate about a line?

Back

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

Front

If the coordinates of two points are (2, -7) and (-1, 6), what is the slope?

Back

The slope is -13/3.