Slope from a Graph

Front

What is the definition of slope in the context of 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 using the rise/run method?

Back

To calculate the slope using the rise/run method, identify two points on the line (x1, y1) and (x2, y2). The slope (m) is calculated as 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 there is no horizontal change (run) while the y-values change.

Front

How can you identify the slope from a graph visually?

Back

You can identify the slope from a graph visually by selecting two points on the line, measuring the vertical distance (rise) and the horizontal distance (run) between them, and calculating the ratio of rise to run.

Front

What is the slope of the line represented by the equation y = 2x + 3?

Back

The slope of the line represented by the equation y = 2x + 3 is 2.

Front

What is the slope of the line represented by the equation y = -1/2x + 4?

Back

The slope of the line represented by the equation y = -1/2x + 4 is -1/2.

Front

What does a slope of 1 indicate about a line?

Back

A slope of 1 indicates that for every unit increase in x, there is a corresponding unit increase in y, resulting in a 45-degree angle line.