Finding Slope from Graphs and Tables

Front

What is slope in mathematics?

Back

Slope is a measure of the steepness or incline of a line, typically represented as 'm' in the equation of a line (y = mx + b). It is calculated as the change in y (rise) over the change in x (run).

Front

How do you calculate the slope from 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 x increases, y 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 x increases, y 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 y regardless of the change in x.

Front

What is the slope of a vertical line?

Back

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

Front

If a line rises 3 units for every 1 unit it runs, what is the slope?

Back

The slope is 3, calculated as rise/run = 3/1.

Front

If a line falls 2 units for every 4 units it runs, what is the slope?

Back

The slope is -1/2, calculated as rise/run = -2/4.

Front

What is the slope of the line represented by the equation y = 4x + 1?

Back

The slope is 4, as it 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 and run between them, and use the formula m = rise/run.