Finding 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 to the horizontal change between two points on the line.

Front

What is the formula to calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The formula for slope (m) is 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, 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

What does an undefined slope mean?

Back

An undefined slope occurs in vertical lines where the change in x is zero, making the slope calculation (y2 - y1) / (x2 - x1) impossible.

Front

What does a slope of zero indicate about a line?

Back

A slope of zero indicates a horizontal line where the y-values remain constant as the x-values change.

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 vertical change (rise) and the horizontal change (run), and then use the slope formula (rise/run).

Front

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

Back

The slope can represent rates of change in various contexts, such as speed, cost per unit, or growth rates, making it essential for interpreting data.

Front

How does the slope relate to linear equations in the form y = mx + b?

Back

In the equation y = mx + b, 'm' represents the slope of the line, while 'b' represents the y-intercept, indicating where the line crosses the y-axis.

Front

What is the slope of a line that is perfectly vertical?

Back

The slope of a perfectly vertical line is undefined.