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 'm' in the equation of a line (y = mx + b). It is calculated as the ratio of the change in the vertical direction (rise) to the change in the horizontal direction (run).

Front

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

Back

The slope (m) can be calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-values increase, the y-values also increase, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-values increase, the y-values decrease, meaning the line falls from left to right.

Front

What does a slope of zero mean?

Back

A slope of zero means that the line is horizontal, indicating that there is no change in the y-value as the x-value changes.

Front

What does an undefined slope mean?

Back

An undefined slope occurs in vertical lines, where the change in x is zero, leading to division by zero in the slope formula.

Front

How can you determine the slope from a graph?

Back

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

Front

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

Back

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

Front

What is the relationship between slope and parallel lines?

Back

Parallel lines have the same slope, meaning they will never intersect and maintain a constant distance apart.

Front

What is the relationship between slope and perpendicular lines?

Back

Perpendicular lines have slopes that are negative reciprocals of each other. If one line has a slope of m, the other will have a slope of -1/m.