Finding Slope from a Graph

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 of a line given 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-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 on a graph?

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, indicating no vertical change as the x-values change.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as it would require division by zero (the change in x is 0).

Front

If a line has a slope of 2/7, what does this mean in terms of rise and run?

Back

A slope of 2/7 means that for every 7 units moved horizontally (run), the line rises 2 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 rise/run ratio.

Front

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

Back

The slope of a perfectly vertical line is undefined.

Front

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

Back

The slope of a perfectly horizontal line is 0.