Slope from ordered pairs and tables

Front

What is the definition of slope in mathematics?

Back

Slope is a measure of the steepness or incline of a line, typically represented as 'm' in the slope-intercept form of a linear equation. It is calculated as the ratio of the change in the y-coordinate to the change in the x-coordinate between two points on the line.

Front

How do you calculate the slope between two points (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-coordinate increases, the y-coordinate also increases, 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-coordinate increases, the y-coordinate decreases, 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-coordinate regardless of the change in the x-coordinate.

Front

What is the slope of a vertical line?

Back

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

Front

Given the points (2, 3) and (5, 11), what is the slope of the line connecting them?

Back

The slope is calculated as m = (11 - 3) / (5 - 2) = 8 / 3.

Front

If a line has a slope of 6, what does this mean in terms of rise over run?

Back

A slope of 6 means that for every 1 unit you move horizontally (run), the line rises 6 units vertically (rise).

Front

What is the slope of the line that passes through the points (8, 9) and (2, 4)?

Back

The slope is calculated as m = (4 - 9) / (2 - 8) = -5 / -6 = 5/6.

Front

How can you determine the slope from a table of values?

Back

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