Slope from Tables

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 (m) = (y2 - y1) / (x2 - x1).

Front

If the slope is positive, what does that indicate about the 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

If the slope is negative, what does that indicate about the 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, 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

Given the points (1, 2) and (3, 6), what is the slope?

Back

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

Front

What does a slope of 1 indicate?

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.

Front

What is the slope of the line represented by the equation y = 3x + 1?

Back

The slope is 3, which means for every unit increase in x, y increases by 3 units.

Front

If a table shows the points (2, 4) and (4, 8), what is the slope?

Back

The slope is (8 - 4) / (4 - 2) = 4 / 2 = 2.