Slope from graphs, tables and Ordered Pairs

Front

What is the definition of slope?

Back

Slope is a measure of the steepness 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 from two ordered pairs (x1, y1) and (x2, y2)?

Back

The 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, as there is no vertical change regardless of the horizontal change.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the horizontal change is 0, leading to division by zero.

Front

Given the points (2, 3) and (4, 7), what is the slope?

Back

Using the formula m = (y2 - y1) / (x2 - x1), the slope is m = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

If a line passes through the points (1, 2) and (3, 6), what is the slope?

Back

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

Front

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

Back

The slope of the line is 3, which is the coefficient of x in the equation.

Front

How can you find the slope from a graph?

Back

To find the slope from a graph, select two points on the line, determine the rise (vertical change) and run (horizontal change), and use the formula m = rise/run.