Slope from a Table

Front

What is the definition of slope?

Back

The slope is a measure of the steepness or incline of a line, calculated as the change in the vertical direction (rise) divided by the change in the horizontal direction (run).

Front

How do you calculate the slope from a table of values?

Back

To calculate the slope from a table, select two points (x1, y1) and (x2, y2) from the table, and use the formula: slope = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate?

Back

A positive slope indicates that as the x-values increase, the y-values also increase, showing a rising line.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the x-values increase, the y-values decrease, showing a falling line.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no change in the y-values regardless of the x-values.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the change in x-values is 0, leading to division by zero.

Front

If the slope is 2, what does this mean in terms of rise and run?

Back

A slope of 2 means that for every 1 unit you move horizontally (run), the line rises 2 units (rise).

Front

What is the slope of the line represented by the points (1, 3) and (4, 9)?

Back

The slope is (9 - 3) / (4 - 1) = 6 / 3 = 2.

Front

If a line has a slope of -1/2, how does it behave?

Back

A slope of -1/2 means that for every 2 units you move horizontally to the right, the line falls 1 unit.

Front

What is the slope of the line represented by the points (2, 5) and (2, 8)?

Back

The slope is undefined because the x-values are the same, indicating a vertical line.