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 to the horizontal change 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 is the slope of a line that rises 4 units for every 5 units it runs?

Back

The slope is 4/5.

Front

If a line has a slope of 5/-2, what does this indicate about its direction?

Back

A slope of 5/-2 indicates that the line descends as it moves from left to right, since the slope is negative.

Front

What is the slope of the line represented by the equation y = 2x + 3?

Back

The slope of the line is 2.

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates that the line is horizontal and does not rise or fall.

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates that the line is vertical.

Front

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

Back

To find 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 passing through the points (1, 8) and (3, 12)?

Back

The slope is 2.

Front

What is the significance of the slope in a real-world context?

Back

In real-world contexts, the slope can represent rates of change, such as speed, growth, or decline.