finding a slope from a graph

Front

What is the definition of slope in a graph?

Back

The slope of a graph 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

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

Front

What does a positive slope indicate about a line on a graph?

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 on a graph?

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 that the line is horizontal, indicating that there is no change in the y-value as the x-value changes.

Front

What does an undefined slope mean?

Back

An undefined slope occurs when a line is vertical, meaning the x-value does not change while the y-value does, leading to division by zero in the slope formula.

Front

If a line rises 3 units for every 2 units it runs, what is the slope?

Back

The slope is 3/2.

Front

If a line falls 2 units for every 4 units it runs, what is the slope?

Back

The slope is -1/2.

Front

How can you determine the slope from a graph visually?

Back

To determine the slope visually, select two points on the line, count the vertical rise and horizontal run between them, and use the rise/run ratio.

Front

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

Back

The slope of a perfectly horizontal line is 0.