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 of a line?

Back

The slope (m) can be calculated using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

What does 'rise over run' mean in the context of slope?

Back

'Rise over run' refers to the vertical change (rise) divided by the horizontal change (run) between two points on a line, which defines the slope.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no vertical change (rise) regardless of the horizontal change (run).

Front

What is the slope of a vertical line?

Back

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

Front

If a line rises 3 units for every 4 units it runs, what is the slope?

Back

The slope is 3/4.

Front

What is the slope of a line that descends from left to right?

Back

The slope is negative, indicating that as the x-values increase, the y-values decrease.

Front

How can you determine the slope from a graph?

Back

To determine the slope from a graph, select two points on the line, count the vertical change (rise) and the horizontal change (run), and then divide rise by run.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does a slope of 1 indicate about a line?

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.