Finding Slope from a Graph Flashcard

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

Back

Slope (m) is 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 regardless of the horizontal change.

Front

What is the slope of a vertical line?

Back

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

Front

If a line has a slope of 3/2, what does this mean in terms of rise and run?

Back

A slope of 3/2 means that for every 2 units of horizontal change (run), the line rises 3 units (rise).

Front

How can you determine the slope from a graph visually?

Back

To determine the slope from a graph, select two points on the line, count the vertical change (rise) and the horizontal change (run), and then calculate the slope using the ratio rise/run.

Front

What is the simplest form of a fraction, and why is it important in slope calculations?

Back

The simplest form of a fraction is when the numerator and denominator have no common factors other than 1. It is important in slope calculations to provide a clear and concise representation of the slope.

Front

What is the slope of a line that rises 4 units for every 1 unit it runs?

Back

The slope of the line is 4/1, which can also be expressed simply as 4.