Finding Slope

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 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 between two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be 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

If a line has a slope of 4, what does this mean in terms of rise and run?

Back

A slope of 4 means that for every 1 unit of horizontal change (run), the line rises 4 units (rise).

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 use the slope formula: m = (y2 - y1) / (x2 - x1).

Front

What is the slope of the line that passes through the points (10, 1) and (5, 2)?

Back

The slope is -1/5, calculated as m = (2 - 1) / (5 - 10).

Front

What is the slope of a line if the rise is 2 and the run is 1?

Back

The slope is 2, calculated as m = rise/run = 2/1.