Slope from a graph Flashcard

Front

What is the definition of slope in a graph?

Back

Slope is a measure of the steepness or incline of a line, calculated 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 between two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1)

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, 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-value increases, the y-value decreases, meaning the line falls from left to right.

Front

What does a slope of zero mean?

Back

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

Front

What does an undefined slope mean?

Back

An undefined slope occurs in vertical lines where the x-value does not change, leading to a division by zero in the slope formula.

Front

If a line has a slope of 5/2, what does this tell you about its steepness?

Back

A slope of 5/2 indicates a steep line that rises 5 units for every 2 units it runs horizontally.

Front

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

Back

The slope of a perfectly horizontal line is 0.

Front

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

Back

The slope of a perfectly vertical line is undefined.

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 rise and horizontal run between them, and calculate the slope using the rise/run formula.