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 to the horizontal change between two points on the line.

Front

How is slope calculated using 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, 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 because the change in x is zero, leading to division by zero.

Front

How can you identify the slope from a graph visually?

Back

The slope can be identified by selecting two points on the line and calculating the rise over run, or by observing the angle of the line relative to the x-axis.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean if a line has an undefined slope?

Back

An undefined slope means the line is vertical, indicating that there is no horizontal change regardless of the vertical change.

Front

How do you determine if a slope is positive, negative, or zero from a graph?

Back

A slope is positive if the line rises from left to right, negative if it falls from left to right, and zero if it is horizontal.