Slope from Graphs and Equations

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 from two points (x1, y1) and (x2, y2)?

Back

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

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the run (horizontal change) is zero.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is zero because there is no vertical change (rise) as you move along the line.

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, resulting in an upward trend.

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, resulting in a downward trend.

Front

How can you determine the slope from the equation of a line in slope-intercept form (y = mx + b)?

Back

In the slope-intercept form, 'm' represents the slope of the line.

Front

What is the slope of the line represented by the equation y = -2x + 4?

Back

The slope of the line is -2.

Front

What is the significance of the slope in real-world applications?

Back

The slope can represent rates of change, such as speed, cost per unit, or growth rates in various contexts.

Front

How do you identify the slope from a graph?

Back

To identify the slope from a graph, select two points on the line, determine the rise and run between them, and calculate the slope using the formula m = rise/run.