Slope from a Table

Front

What is the 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 (m) = (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 an upward trend.

Front

What does a negative slope indicate?

Back

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

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 -2/3, what does this mean in terms of rise and run?

Back

A slope of -2/3 means that for every 3 units you move to the right (run), you move down 2 units (rise).

Front

How can you identify the slope from a graph?

Back

To identify the slope from a graph, pick two points on the line, determine the rise and run between them, and calculate the slope using the formula: slope = rise/run.

Front

What is the slope of the line represented by the points (1, 2) and (4, 5)?

Back

The slope is (5 - 2) / (4 - 1) = 3/3 = 1.

Front

What is the significance of the slope in real-world applications?

Back

The slope can represent rates of change, such as speed, cost per item, or growth rates in various contexts.