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

Slope (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 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-values change.

Front

What does an undefined slope mean?

Back

An undefined slope occurs in a vertical line where the x-values are constant, indicating that there is no horizontal change.

Front

If a line has a slope of 1, what does this imply about the rise and run?

Back

A slope of 1 means that for every unit of rise, there is an equal unit of run, resulting in a 45-degree angle with the x-axis.

Front

What is the slope of a line that goes through the points (2, 3) and (4, 7)?

Back

Slope = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

If a line has a slope of -2, what does this indicate about its direction?

Back

A slope of -2 indicates that for every 2 units the line rises, it runs 1 unit to the left, creating a steep downward angle.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.