Slope = Rise over Run

Front

What is the definition of slope in mathematics?

Back

Slope is a measure of the steepness or incline of a line, defined 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 given 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 is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no vertical change (rise) regardless of the horizontal change (run).

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the horizontal change (run) is 0, leading to division by zero.

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 (vertical change) and run (horizontal change) between them, and use the slope formula: m = rise/run.

Front

What is the relationship between slope and linear equations?

Back

In a linear equation of the form y = mx + b, 'm' represents the slope of the line, and 'b' represents the y-intercept.

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

How does the slope affect the graph of a linear equation?

Back

The slope determines the angle and direction of the line on the graph; a steeper slope indicates a steeper line, while a slope of 0 indicates a horizontal line.